http://sites.science.oregonstate.edu/portfolioswiki/ 2020-01-27T10:20:22-08:00 http://sites.science.oregonstate.edu/portfolioswiki/ http://sites.science.oregonstate.edu/portfolioswiki/lib/images/favicon.ico text/html 1969-12-31T16:00:00-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:DivCurl?rev= text/html 1969-12-31T16:00:00-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:DivCurla?rev= text/html 1969-12-31T16:00:00-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:DivCurlb?rev= text/html 2017-09-29T16:22:36-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:affirmation?rev=1506727356 Read the following list of values and think about each one: athletic ability, being good at art, being smart or getting good grades, creativity, independence, living in the moment, membership in a social group (such as your community, racial group, or school club), music, politics, relationships with friends or family, religious values, and sense of humor. text/html 2015-10-16T14:33:05-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:amperecylinder?rev=1445031185 In this problem, you will be investigating a cylindrical wire of finite thickness $R$, carrying a non-uniform current density $J=\kappa r$, where $\kappa$ is a constant and $r$ is the distance from the axis of the cylinder.\\ text/html 2015-10-16T14:33:05-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:amperecylindera?rev=1445031185 Find the total current flowing through the wire.\\ text/html 2015-10-16T14:33:05-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:amperecylinderb?rev=1445031185 Find the current flowing through Disk 2, a central (circular cross-section) portion of the wire out to a radius $r_2<R$.\\ [Figure: cross section of wire] text/html 2015-10-16T14:33:05-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:amperecylinderc?rev=1445031185 Use Amp\`ere's law to find the magnetic field at a distance $r_1$ outside the wire.\\ text/html 2015-10-16T14:33:05-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:amperecylinderd?rev=1445031185 Use Amp\`ere's law to find the magnetic field at a distance $r_2$ inside the wire.\\ text/html 2019-04-21T22:13:33-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:amperelawdifferential?rev=1555910013 Find the volume current density that produces the following magnetic field (expressed in cylindrical coordinates): \[ \vec{B}(\vec{r})=\begin{cases} \frac{\mu_0\,I\,s}{2\pi a^2}\hat{\phi}& s\leq a \\ \frac{\mu_0\,I}{2\pi s}\hat{\phi}& a<s<b \\ 0& s>b \\ \end{cases} \] text/html 2012-10-26T18:10:06-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:apracticea?rev=1351300206 %Adapted from Colorado Clicker Questions For the following situation, what will the observer see for the direction of $\vec{A}$? For the direction of $\vec{B}$? \medskip \centerline{\includegraphics[scale=0.65]{\TOP Figures/vfapracticea}} \medskip text/html 2012-10-26T18:10:06-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:apracticeb?rev=1351300206 %Adapted from Colorado Clicker Questions The arrows below represent the vector potential $\vec{A}$ (where $|\vec{A}|$ is the same everywhere). Is there a non-zero $\vec{B}$ in the dashed region? If so, what direction does it point? How do you know? \\ text/html 2012-10-26T18:10:06-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:bdirection?rev=1351300206 %Adapted from Colorado Clicker Questions What is $\vec{B}$ at the point $S$? \medskip \centerline{\includegraphics[scale=0.5]{\TOP Figures/vfbdirection}} \medskip text/html 2016-04-05T10:47:39-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:bfinitelinea?rev=1459878459 Find the magnetic field for a finite segment of straight wire, carrying a uniform current $I$. Put the wire on the $z$ axis, from $z_1$ to $z_2$. text/html 2016-04-05T10:47:39-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:bfinitelineb?rev=1459878459 Show that your answer to part (a) is the curl of the magnetic vector potential. text/html 2012-10-26T18:10:06-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:biotsavartchallenge?rev=1351300206 In class, we found that the magnetic vector potential created by a rotating ring of charge (total charge $Q$, radius $R$, rotating with period $T$) everywhere in space is\\ \begin{equation*} \vec{A}(\vec{r}) =\frac{\mu_0}{4 \pi}\frac{Q\,R}{T}\,\hat{\phi}\int_0^{2 \pi} \dfrac{\cos\phi'\,d\phi'}{\sqrt{r^2+R^2-2 r R cos\phi'+z^2}} \end{equation*}\\ text/html 2013-05-09T13:02:00-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:biotsavartcoils?rev=1368129720 Two charged rings of radius $R$ spin in opposite directions, each with total current $I$. They are placed a distance $2L$ apart and oriented as shown below. \medskip \centerline{\includegraphics[scale=0.65]{\TOP Figures/vfbiotsavartcoils}} \medskip text/html 2013-05-09T13:02:00-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:biotsavartcoilsa?rev=1368129720 What is the magnetic field on the $z$-axis due to Loop 1? text/html 2013-05-09T13:02:00-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:biotsavartcoilsb?rev=1368129720 What is the magnetic field on the $z$-axis due to Loop 2? text/html 2013-05-09T13:02:00-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:biotsavartcoilsc?rev=1368129720 What is the leading non-zero term for the total magnetic field on the $z$-axis near the midpoint between the coils ($z<<R$)? text/html 1969-12-31T16:00:00-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:biotsavartlimitSJP?rev= text/html 1969-12-31T16:00:00-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:biotsavartlimitaSJP?rev= text/html 2012-10-31T17:31:12-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:biotsavartlimitambk?rev=1351729872 Take the limit $r>>R$ in the plane of the ring, and simplify to find the {\it leading} non-zero term. Briefly describe any checks you did to validate your answer.\\ text/html 1969-12-31T16:00:00-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:biotsavartlimitbSJP?rev= text/html 2012-10-31T17:31:12-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:biotsavartlimitbmbk?rev=1351729872 Find the \emph{leading} non-zero term for $|\vec{r}|<<R$ (\emph{i.e.} not on-axis). Briefly describe any checks you did to validate your answer.\\ text/html 2012-10-26T18:10:06-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:biotsavartlimitchallenge?rev=1351300206 In problem 1, you found the approximation for $\vec{B}$ from a spinning ring of charge when you are near and far away \emph{on the x-axis}. Now, find the \emph{leading} non-zero term for $r<<R$ at some generic $\vec{r}$ (\emph{i.e.} not on-axis). \begin{equation*} \vec{B}(\vec{r}) =\frac{\mu_0}{4 \pi}\frac{Q\,R}{T}\int_0^{2 \pi} \dfrac{z\,\cos\phi'\,\hat{r}+\left(R-r cos\phi'\right)\hat{z}}{\left(r^2+R^2-2 r R cos\phi'+z^2\right)^{3/2}}d\phi'\, \end{equation*} text/html 2015-10-16T14:31:48-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:biotsavartlimitmbk?rev=1445031108 In class we derived an expression, using the Biot-Savart law, for the magnetic field created by a rotating ring of charge (total charge $Q$, radius $R$, rotating with period $T$) everywhere in space.\\ \begin{eqnarray*} \vec{B}(\vec{r}) =\frac{\mu_0}{4 \pi} \frac{Q\,R}{T} \int_0^{2 \pi} \frac{z\,\cos\phi' \, \hat{r}+\left(R-r \cos\phi'\right)\hat{z}}{\left(r^2+R^2-2 r R \cos\phi'+z^2\right)^{3/2}}d\phi'\, \end{eqnarray*}\\ text/html 2009-10-17T14:03:18-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:biotsavartsquare?rev=1255813398 Consider a point a distance $z$ above the center of an infinitesimally thin, square sheet of current. The current is parallel to one of the square sides. (Obviously, since the current cannot just begin and end in the middle of nowhere, this current is just the building block for some larger current.) text/html 2011-12-06T16:11:47-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:biotsavartsquarea?rev=1323216707 Use the Biot-Savart Law to find the magnetic field at the point $z$. You may use any symmetry arguments you like, but do not use Ampere's Law. Note: if you choose to use Mathematica or Maple to evaluate the integral, it may take you into complex number land, even though the integral is clearly real. To address this issue, you should be explicit about what assumptions you want the program to make (``Assume'' in Maple and ``Assumptions'' in Mathematica) text/html 2011-12-06T16:11:47-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:biotsavartsquareb?rev=1323216707 Consider your previous answer in the limit that the square becomes infinitely large. text/html 2011-12-06T16:11:47-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:biotsavartsquarec?rev=1323216707 Discuss your answer in the light of the magnetic field above an infinite sheet of current as found using Ampere's Law. text/html 2012-10-26T18:10:06-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:bmethod?rev=1351300206 %Adapted from Colorado Clicker Questions An electron is moving in a straight line with constant speed v. What method would you use to calculate the B-field generated by this electron? \medskip \centerline{\includegraphics[scale=0.65]{\TOP Figures/vfbmethod}} \medskip text/html 2012-10-26T18:10:06-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:bsymmetry?rev=1351300206 %Adapted from Colorado Clicker Questions Which of the below B-field components are not possible? How do you know? \medskip \centerline{\includegraphics[scale=0.5]{\TOP Figures/vfbsymmetry}} \medskip text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:capacitor?rev=1350110878 We know that the electric field everywhere in space due to an infinite plane of charge with charge density located in the $xy$-plane at $z=0$ is \begin{equation*} \EE(z) = \begin{cases}\displaystyle +{\sigma\over2\epsilon_0}\>\zhat & z>0 \cr \noalign{\smallskip}\displaystyle -{\sigma\over2\epsilon_0}\>\zhat & z<0 \end{cases} \end{equation*} text/html 2009-10-17T13:40:34-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:capacitora?rev=1255812034 Sketch the $z$-component of the electric field as a function of $z$. text/html 2009-10-17T14:16:05-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:capacitorb?rev=1255814165 Draw a similar picture, and write a function that expresses the electric field everywhere in space, for an infinite conducting slab in the $xy$-plane, of thickness $d$ in the $z$-direction, that has a charge density $+|\sigma|$ on each surface. text/html 2009-10-17T13:40:34-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:capacitorc?rev=1255812034 Repeat for a charge density $-|\sigma|$ on each surface. text/html 2009-10-17T13:40:34-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:capacitord?rev=1255812034 Now imagine two {\bf conductors}, one each of the two types described above, separated by a distance $L$. Use the principle of superposition to find the electric field everywhere. Discuss whether your answer is reasonable. Does it agree with the known fact that the electric field inside a conductor is zero? Has superposition been correctly applied? Is Gauss' Law correct? Try to resolve any inconsistencies. text/html 2016-08-25T13:33:07-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:chargegraph?rev=1472157187 The following graph represents the charge density on a thin piece of plastic (dielectric). Find the charge on the segment between centimeter 3 and centimeter 10. [Figure: cross section of wire] text/html 2012-09-23T14:04:57-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:circlevector?rev=1348434297 Consider the geometry of $\vert \rr-\rrp\vert$. text/html 2016-09-23T15:42:11-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:circlevectora?rev=1474670531 Make a sketch of the graph $$ \vert \Vec r - \Vec a \vert = 2 $$ for each of the following values of $\Vec a$: $$ \begin{eqnarray} \Vec a &=& \Vec 0\\ \Vec a &=& 2 \hat \imath- 3 \hat \jmath\\ \Vec a &=& \hbox{points due east and is 2 units long} \end{eqnarray} $$ text/html 2010-10-17T09:18:54-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:circlevectorb?rev=1287332334 Derive a more familiar equation equivalent to $$ \vert \Vec r - \Vec a \vert = 2 $$ for arbitrary $\Vec a$, by expanding $\Vec r$ and $\Vec a$ in rectangular coordinates. Simplify as much as possible. (Ok, ok, I know this is a terribly worded question. What do I mean by ``more familiar”? What do I mean by ``simplify as much as possible”? Why am I making you read my mind? Try it anyway. Real life is not full of carefully worded problems. Bonus points to anyone who can figure out a better… text/html 2010-10-17T09:18:54-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:circlevectorc?rev=1287332334 Write a brief description of the geometric meaning of the equation $$ \vert \Vec r - \Vec a \vert = 2 $$ text/html 2018-03-30T09:54:38-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:circlevectorpre?rev=1522428878 Make sketches of the following functions, by hand, all on the same axes. Briefly describe, using good scientific writing that includes both words and equations, the role that the number 2 plays in the shape of the second graph: \begin{eqnarray} y &=& \sin x\\ y &=& \sin(2+x) \end{eqnarray} text/html 2015-09-23T18:12:15-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:complexnum?rev=1443057135 For the following expressions, determine the complex conjugate, square, and norm. Plot and clearly label each on an Argand diagram. text/html 2015-09-23T18:12:15-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:complexnuma?rev=1443057135 $z_1=4i-3$ text/html 2015-09-23T18:12:15-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:complexnumb?rev=1443057135 $z_2=5e^{-i\pi/3}$ text/html 2015-09-23T18:12:15-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:complexnumc?rev=1443057135 $z_3=-8$ text/html 2015-09-23T18:12:15-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:complexnumd?rev=1443057135 In a few full sentences, explain the geometric meaning of the complex conjugate and norm. text/html 2015-10-01T11:38:26-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:complexrectangularpractice?rev=1443724706 If $z_1=5e^{7i\pi/4}$, $z_2=3e^{-i\pi/2}$, and $z_3=9e^{(1+i\pi)/3}$, express each of the following complex numbers in rectangular form, i.e. in the form $x+iy$ where $x$ and $y$ are real. text/html 2015-10-01T11:38:26-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:complexrectangularpractice2?rev=1443724706 %Boas 2.9 (parts thereof) Express each of the following complex numbers in exponential form, i.e. in the form $r e^{i\phi}$ where $r$ and $\phi$ are real. text/html 2015-10-01T11:38:26-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:complexrectangularpracticea?rev=1443724706 $z_1 +z_2$ text/html 2015-10-01T11:38:26-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:complexrectangularpracticeb?rev=1443724706 $z_1 z_2$ text/html 2015-10-01T11:38:26-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:complexrectangularpracticec?rev=1443724706 $\frac{z_2}{z_3}$ text/html 2015-10-01T11:38:26-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:complexrectangularpracticed?rev=1443724706 $\left(1+i\sqrt{3}\right)^{6}$ text/html 2015-10-01T11:38:26-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:complexrectangularpracticee?rev=1443724706 $\frac{2+3i}{1-i}$ text/html 2012-10-31T17:31:12-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:conductorsgem235?rev=1351729872 A metal sphere of radius $R$, carrying charge $q$ is surrounded by a thick concentric metal shell (inner radius $a$, outer radius $b$, as shown below). The shell carries no net charge. \medskip \centerline{\includegraphics[scale=1]{\TOP Figures/vfconductor}} \medskip text/html 2009-10-17T13:40:34-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:conductorsgem235a?rev=1255812034 Find the surface charge density $\sigma$ at $R$, at $a$, and at $b$. text/html 2018-05-02T17:18:45-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:conductorsgem235b?rev=1525306725 Find $E_r$, the radial component of the electric field and plot it as a function of $r$. Are the discontinuities in the electric field related to the charge density in the way you expect from previous problems? text/html 2009-10-17T13:40:34-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:conductorsgem235c?rev=1255812034 Find the potential at the center of the sphere, using infinity as the reference point. text/html 2009-10-17T14:27:17-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:conductorsgem235d?rev=1255814837 Now the outer surface is touched to a grounding wire, which lowers its potential to zero (the same as infinity). How do your answers to a), b), and c) change? text/html 2015-10-16T11:05:06-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:conductorsgem235modb?rev=1445018706 Find $E_r$, the radial component of the electric field and plot it as a function of $r$. %Are the discontinuities in the electric field what you expect from our unit on boundary conditions? Explain. text/html 2009-08-21T07:20:50-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:conesurface?rev=1250864450 Using integration, find the surface area of a cone. text/html 2016-10-07T12:07:55-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:contours?rev=1475867275 Shown below is a contour plot of a scalar field, $\mu(x,y)$. Assume that $x$ and $y$ are measured in meters and that $\mu$ is measured in kilograms. Four points are indicated on the plot.\\ \medskip \centerline{\includegraphics[scale=1]{\TOP Figures/contoursfig1}} \medskip text/html 2020-01-24T19:13:42-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:contoursa?rev=1579922022 Determine $\frac{\partial\mu}{\partial x}$ and $\frac{\partial\mu}{\partial y}$ at each of the four points. text/html 2016-10-07T12:07:55-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:contoursb?rev=1475867275 On a printout of the figure, draw a qualitatively accurate vector at each point corresponding to the gradient of $\mu(x,y)$ using your answers to part a above. How did you choose a scale for your vectors?\\ \\ Describe how the direction of the gradient vector is related to the contours on the plot and what property of the contour map is related to the magnitude of the gradient vector. text/html 2016-10-10T12:49:10-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:contoursc?rev=1476128950 Evaluate the gradient of $h(x,y)=(x+1)^2(\frac{x}{2}-\frac{y}{3})^3$ at the point $(x,y)=(3,-2)$. text/html 2016-10-10T12:49:10-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:contoursd?rev=1476128950 \medskip \centerline{\includegraphics[scale=1]{\TOP Figures/contoursfig2}} \medskip A contour map for a different function is shown above. On a printout of this contour map, sketch a field vector map of the gradient of this function (sketch vectors for at least 10 different points). The direction and magnitude of your vectors should be qualitatively accurate, but do not calculate the gradient for this function. text/html 2019-04-13T08:58:46-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:cosmicasimov?rev=1555171126 You are part of the team building Cosmic AC, Asimov's ultimate, universe-sized computer. Your job is to fabricate a charged disk, 10 meters in radius and 1 cm thick. The charge density on the disk should be: $$\rho=\alpha e^{-\beta s^2} \cos(\gamma z)$$ text/html 2009-08-22T13:50:48-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:cosmicasimova?rev=1250974248 What is the total charge on the disk, in terms of the parameters $\alpha$, $\beta$, and $\gamma$? text/html 2009-08-22T13:50:48-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:cosmicasimovb?rev=1250974248 What are the dimensions of $\alpha$, $\beta$, and $\gamma$? text/html 2010-11-07T05:24:09-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:cosmicasimovc?rev=1289136249 Design specifications indicate that: the maximum charge density should be $27 ~\frac{C}{cm^3}$, only one-half period of the $\cos(\gamma z)$ term spans the whole height of the disk, the upper and lower circular surfaces have zero charge density, and the maximum values of the charge density on the circumference of the disk should be 10 percent of the maximum in the center. Find values for $\alpha$, $\beta$, and $\gamma$. text/html 2009-08-22T13:50:48-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:cosmicasimovd?rev=1250974248 What is the total charge on the disk? text/html 2019-04-13T08:58:46-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:cosmicasimove?rev=1555171126 Estimate how much error your would make in your calculation of the total charge density if you assumed that the disk was infinitely wide. (Keep the same functional dependence for the charge density, i.e. do not change the values of $\alpha$, $\beta$, and $\gamma$.) text/html 2011-11-22T18:33:12-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:cosmicasimovf?rev=1322015592 Given the relative sizes of the radius of the disk and the thickness of the disk, it might be reasonable to approximate the disk as infinitely thin. In this case, you might want to describe the charge density as a surface charge density $\sigma$ rather than as a volume charge density $\rho$. From the given volume charge density $\rho$, find an equivalent surface charge density. text/html 2011-02-22T11:24:02-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:crosstriangle?rev=1298402642 Use the cross product to find the components of the unit vector $\hat n$ perpendicular to the plane shown in the figure below, i.e.~ the plane joining the points $\{(1,0,0),(0,1,0),(0,0,1)\}$. [Figure: a plane] text/html 2010-09-19T10:50:55-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:cubecharge?rev=1284918655 Charge is distributed on the surface of a dielectric cube with charge density $\sigma=\alpha z$, where $z$ is the height from the bottom of the cube, and where each side of the cube has length $L$. What is the total charge on the cube? Don't forget about the top and bottom of the cube. text/html 2015-10-01T11:38:26-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:cubechargea?rev=1443724706 Charge is distributed throughout the volume of a dielectric cube with charge density $\rho=\beta z^2$, where $z$ is the height from the bottom of the cube, and where each side of the cube has length $L$. What is the total charge inside the cube? Do this problem in two ways as both a single integral and as a triple integral. text/html 2015-10-01T11:38:26-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:cubechargeb?rev=1443724706 Charge is distributed on the surface of a dielectric cube with charge density $\sigma=\alpha z$, where $z$ is the height from the bottom of the cube, and where each side of the cube has length $L$. What is the total charge on the cube? Don't forget about the top and bottom of the cube. text/html 2012-10-31T17:31:28-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:curldivergencefree?rev=1351729888 %Adapted from Colorado Clicker Questions 4 and 5 Below are cross-sections for several vector fields (assume each cross-section is the same). %For this problem, explanations will count for the majority of the points. \medskip \centerline{\includegraphics[scale=0.65]{\TOP Figures/vfefield} \includegraphics[scale=0.65]{\TOP Figures/vfbfield} \includegraphics[scale=0.65]{\TOP Figures/vfnofield}} \centerline{(I)\hspace{1.3in}(II)\hspace{1.3in}(III)} \medskip text/html 2012-10-31T17:31:28-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:curldivergencefreea?rev=1351729888 If the above sketches represent an electric field, \begin{enumerate} \item Which \emph{violate} one of Maxwell's Equations within the region shown? \item For those that do not violate Maxwell's equations, what charge distribution would be needed to generate this field and where would it be located? \end{enumerate} text/html 2012-10-31T17:31:28-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:curldivergencefreeb?rev=1351729888 If the above sketches represent a magnetic field, \begin{enumerate} \item Which \emph{violate} one of Maxwell's Equations within the region shown? \item For those that do not violate Maxwell's equations, what charge distribution would be needed to generate this field and where would it be located? \end{enumerate} text/html 2013-05-09T13:02:00-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:curlfree?rev=1368129720 %Adapted from Colorado Clicker Questions 4 and 5 Below are two sketches of electric field lines. For this problem, explanations will count for the majority of the points. \medskip \centerline{\includegraphics[scale=0.65]{\TOP Figures/vfcurlfree}} \medskip text/html 2013-05-09T13:02:00-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:curlfreea?rev=1368129720 Which of the above sketches show field lines that \emph{violate} one of Maxwell's Equations within the region bounded by the dashed lines? How do you know? text/html 2013-05-09T13:02:00-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:curlfreeb?rev=1368129720 For those that do not violate Maxwell's Equations, what current would be needed to generate the field and where would it be located? text/html 2011-11-22T18:33:12-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:curlpractice2?rev=1322015592 Choose some simple vector fields of your own and find the curl of them both by hand and using Mathematica or Maple. Choose some that are written in terms of rectangular coordinates and others in cylindrical and/or spherical. text/html 2013-10-29T20:12:27-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:curlpracticemmm?rev=1383102747 Calculate the curl of each of the following vector fields. You may look up the formulas for curl in curvilinear coordinates. text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:curlpracticemmma?rev=1350110878 $\FF=z^2\,\hat{x} + x^2 \,\hat{y} -y^2 \,\hat{z}$ text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:curlpracticemmmb?rev=1350110878 $\GG = e^{-x} \,\hat{x} + e^{-y} \,\hat{y} +e^{-z} \,\hat{z}$ text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:curlpracticemmmc?rev=1350110878 $\HH = yz\,\hat{x} + zx\,\hat{y} + xy\,\hat{z}$ text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:curlpracticemmmd?rev=1350110878 $\II = x^2\,\hat{x} + z^2\,\hat{y} + y^2\,\hat{z}$ text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:curlpracticemmme?rev=1350110878 $\JJ = xy\,\hat{x} + xz\,\hat{y} + yz\,\hat{z}$ text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:curlpracticemmmend?rev=1350110878 For each vector field in the preceding problems which have zero curl, find the corresponding potential function. text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:curlpracticemmmf?rev=1350110878 Compare the curl to the divergence for each field (see Homework 2 Practice). text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:curlvisualizepractice?rev=1350110878 If you need more practice visualizing curl, go through the Mathematica Notebook on the course website. text/html 2019-07-10T15:55:00-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:currentpractice?rev=1562799300 %Adapted from Colorado Clicker Questions *Redraw the figure for this problem and reword the problem by labeling the width of the ribbon something other than a (which seems like area, not length) AND use the same font in the figure as in the text.* A ``ribbon'' (width $a$) of surface current flows with surface current density $\vec{K}$. Right next to it is a second identical ribbon of current. text/html 2019-07-10T15:55:00-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:currentpracticea?rev=1562799300 Viewed collectively, what is the new total surface current density? text/html 2019-07-10T15:55:00-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:currentpracticeb?rev=1562799300 Viewed collectively, what is the new total current in terms of the original current density? text/html 2014-10-10T16:05:42-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:dadtaumemorizea?rev=1412982342 Write down $\vec{dA}$ for each of the surfaces of a rectangular prism, a finite cylinder, and a sphere. text/html 2014-10-10T16:05:42-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:dadtaumemorizeb?rev=1412982342 Write down $d\tau$ in rectangular, cylindrical, and spherical coordinates. text/html 2009-09-30T08:49:24-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:delta?rev=1254325764 The linear charge density from a series of charges along the $x$-axis is given by: $$\lambda(x) = \sum_{n=0}^{10} q_0 \, n^2 \delta\!\left(x-{n\over 10}\right)$$ text/html 2019-04-13T08:58:46-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:deltaa?rev=1555171126 Write a sentence or two indicating describing the dimensions of each term in this equation, including any constants (for which the dimensions have not been indicated). text/html 2009-09-30T08:49:24-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:deltab?rev=1254325764 What is the total charge on the $x$-axis? text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:deltapractice?rev=1350110878 You have a charge distribution composed of two point charges: one with charge $+3q$ located at $x=-d$ and the other with charge $-q$ located at $x=+d$. text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:deltapractice2?rev=1350110878 Sketch the volume charge density: $\rho (x,y,z)=c\,\delta (x-3)$ text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:deltapracticea?rev=1350110878 Sketch the charge distribution. text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:deltapracticeb?rev=1350110878 Write an expression for the \emph{volume} charge density $\rho (\vec{r})$ everywhere in space. text/html 2014-10-01T17:53:19-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:derivrules?rev=1412211199 Make sure that you can find the derivative of all of the common transcendental functions: power, trig, exponential, logs. text/html 2010-10-17T09:18:54-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:dimensions?rev=1287332334 When physicists calculate the value of a physical quantity from an equation, they pay particular attention to the units involved. A force of 2 is ill-defined, a force of 2 Newtons is clear. When physicists want to check the plausibility of an equation, without worrying exactly about which set of units will be used (e.g. Newtons vs. pounds vs. dynes), they often look at the ``dimensions” of the physical quantities involved. ``Dimension” refers to the powers of the basic physical quantities… text/html 2011-11-22T18:33:12-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:directionalderivative?rev=1322015592 Imagine you're standing on a landscape with a local topology described by the function $f(x, y)= k x^{2}y$, where $k=20 \frac{m}{km^3}$ is a constant, $x$ and $y$ are east and north coordinates, respectively, with units of kilometers. You're standing at the spot (3 km,2 km) and there is a cottage located at (1 km, 2 km). At the spot you're standing, what is the slope of the ground in the direction of the cottage? Plot the function $f(x, y)$ in Mathematica. Does your result makes sense from the g… text/html 2016-10-07T11:35:03-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:distancecurvilinear?rev=1475865303 The distance $\left\vert\Vec r -\Vec r\,{}'\right\vert$ between the point $\Vec r\,{}'=(x\,{}',y\,{}',z\,{}')$ and the point $\Vec r=(x,y,z)$ is a coordinate-independent, physical and geometric quantity. But, in practice, you will need to know how to express this quantity in different coordinate systems. text/html 2018-04-04T15:56:18-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:distancecurvilineara?rev=1522882578 Find the distance $\left\vert\Vec r -\Vec r\,{}'\right\vert$ between the point $\Vec r\,{}'=(x\,{}',y\,{}',z\,{}')$ and the point $\Vec r=(x,y,z)$ in rectangular coordinates. text/html 2018-04-04T15:56:18-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:distancecurvilinearb?rev=1522882578 Show that this same distance written in cylindrical coordinates is: $$ \left|\Vec r -\Vec r\,{}'\right| =\sqrt{s^2+s\,{}'^2-2ss\,{}'\cos(\phi\,{}'-\phi) +(z\,{}'-z)^2} $$ text/html 2018-04-12T09:15:17-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:distancecurvilinearc?rev=1523549717 Show that this same distance written in spherical coordinates is: $$ \left\vert\Vec r\,{}' -\Vec r\right\vert =\sqrt{r\,{}'^2+r^2-2rr\,{}' \left[\sin\theta\sin\theta\,{}'\cos(\phi\,{}'-\phi) +\cos\theta\,{}'\cos\theta\right]} $$ text/html 2018-04-04T15:56:18-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:distancecurvilineard?rev=1522882578 Now assume that $\Vec r\,{}'$ and $\Vec r$ are in the $x$-$y$ plane. Simplify the previous two formulas. text/html 2013-05-09T13:02:00-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:divergencefree?rev=1368129720 %Adapted from Colorado Clicker Questions 4 and 5 Below are several sketches of magnetic field lines. For this problem, explanations will count for the majority of the points. \medskip \centerline{\includegraphics[scale=0.65]{\TOP Figures/vfdivergencefree}} \medskip text/html 2013-05-09T13:02:00-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:divergencefreea?rev=1368129720 Which of the above sketches show field lines that \emph{violate} one of Maxwell's Equations within the region bounded by the dashed lines? How do you know? text/html 2013-05-09T13:02:00-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:divergencefreeb?rev=1368129720 For those that do not violate Maxwell's Equations, what current would be needed to generate the field and where would it be located? text/html 2013-10-29T20:12:27-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:divergencepractice?rev=1383102747 Calculate the divergence of each of the following vector fields. You may look up the formulas for divergence in curvilinear coordinates. text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:divergencepractice2?rev=1350110878 Choose some simple vector fields of your own and find the divergence of them both by hand and using Mathematica or Maple. Choose some that are written in terms of rectangular coordinates and others in cylindrical and/or spherical. text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:divergencepracticea?rev=1350110878 $\FF=z^2\,\hat{x} + x^2 \,\hat{y} -y^2 \,\hat{z}$ text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:divergencepracticeb?rev=1350110878 $\GG = e^{-x} \,\hat{x} + e^{-y} \,\hat{y} +e^{-z} \,\hat{z}$ text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:divergencepracticec?rev=1350110878 $\HH = yz\,\hat{x} + zx\,\hat{y} + xy\,\hat{z}$ text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:divergencepracticed?rev=1350110878 $\II = x^2\,\hat{x} + z^2\,\hat{y} + y^2\,\hat{z}$ text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:divergencepracticee?rev=1350110878 $\JJ = xy\,\hat{x} + xz\,\hat{y} + yz\,\hat{z}$ text/html 2013-10-29T20:12:27-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:divergencepracticef?rev=1383102747 $\KK = s^2\,\hat{s}$ text/html 2013-10-29T20:12:27-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:divergencepracticeg?rev=1383102747 $\LL = r^3\,\hat{\phi}$ text/html 2013-10-29T20:12:27-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:divergencepracticeh?rev=1383102747 $\MM = r^3 \cos{\phi}\,\hat{r} + \frac{1}{r^2} \sin^2{\theta}\,\hat{\phi}$ text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:divergenceprism?rev=1350110878 Consider the vector field $\Vec F=(x+2)\hat{x} +(z+2)\hat{z}$. text/html 2010-10-17T09:18:54-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:divergenceprisma?rev=1287332334 Calculate the divergence of $\Vec F$. text/html 2010-10-17T09:18:54-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:divergenceprismb?rev=1287332334 In which direction does the vector field $\Vec F$ point on the plane $z=x$? What is the value of $\Vec F\cdot \hat n$ on this plane where $\hat n$ is the unit normal to the plane? text/html 2011-02-22T11:24:02-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:divergenceprismc?rev=1298402642 Verify the divergence theorem for this vector field where the volume involved is drawn below. [Figure: Volume for divergence %*theorem.] text/html 2019-04-21T22:13:33-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:divergencespherical?rev=1555910013 The gravitational field due to a spherical shell of matter (or equivalently, the electric field due to a spherical shell of charge) is given by: \begin{equation} \Vec g = \begin{cases} 0&\textrm{for } r<a\\ -G \,\frac{M}{b^3-a^3}\, \left( r-\frac{a^3}{r^2}\right)\, \hat r & \textrm{for } a<r<b\\ text/html 2009-10-01T08:03:54-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:divergencesphericala?rev=1254409434 Using the given value of the gravitational field, find the divergence of the gravitational field everywhere in space. You will need to divide this question up into three parts: $r<a$, $a<r<b$, and $r>b$. text/html 2009-10-01T08:03:54-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:divergencesphericalb?rev=1254409434 Discuss the physical meaning of the divergence in this particular example. text/html 2009-10-01T08:03:54-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:divergencesphericalc?rev=1254409434 For this gravitational field, verify the divergence theorem on a sphere, concentric with the shell, with radius $Q$, where $a<Q<b$. text/html 2009-10-01T08:03:54-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:divergencesphericald?rev=1254409434 Discuss how this example would change if you were discussing the electric field of a uniformly charged spherical shell. text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:divergencevisualizepractice?rev=1350110878 If you need more practice visualizing divergence, go through the Mathematica notebook on the course website. text/html 2014-10-08T15:44:19-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:drvecmemorize?rev=1412808259 Give the expression for $d\vec{r}$ in rectangular, cylindrical, and spherical coordinates. text/html 2018-04-18T11:07:48-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:efiniteline?rev=1524074868 Consider the finite line with a uniform charge density from class. text/html 2018-04-18T11:07:48-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:efinitelinea?rev=1524074868 Write an integral expression for the electric field at any point in space due to the finite line. In addition to your usual physics sense-making, you must include a clearly labeled figure and discuss what happens to the direction of the unit vectors as you integrate. text/html 2018-04-18T11:07:48-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:efinitelineb?rev=1524074868 Perform the integral to find the $z$-component of the electric field. In addition to your usual physics sense-making, you must compare your result to the gradient of the electric potential we found in class. (If you want to challenge yourself, do the $s$-component as well!) text/html 2011-12-06T13:04:26-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:energygem231?rev=1323205466 Three charges are situated at the corners of a square (side $s$). Two have charge $-q$ and are located on opposite corners. The third has charge $+q$ and is opposite an empty corner. text/html 2011-12-06T13:04:26-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:energygem231a?rev=1323205466 How much work does it take to bring in another charge, $+q$, from far away and place it at the fourth corner? text/html 2011-12-06T13:04:26-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:energygem231b?rev=1323205466 How much work does it take to assemble the whole configuration of four charges? text/html 2011-12-06T14:57:34-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:energygem234?rev=1323212254 Consider two concentric spherical shells, of radii $a$ and $b$. Suppose the inner one carries a charge $q$, and the outer one a charge $-q$ (both of them uniformly distributed over the surface). Calculate the energy of this configuration. text/html 2011-12-06T14:57:34-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:energygem234a?rev=1323212254 Starting from: $$W= {\epsilon_0\over 2}\int_{\hbox{all space}}E^2 \, d\tau$$ text/html 2016-04-05T10:42:36-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:energygem234b?rev=1459878156 Starting from: $$W= W_1 + W_2 + \epsilon_0\int_{\hbox{all space}}\left(\vec E_1\cdot\vec E_2\right)\, d\tau$$ and using the result that the total energy of a uniformly charged spherical shell of total charge $q$ and radius $R$ is: $$W_{total}={1 \over 8 \pi\epsilon_0}{q^2 \over R}$$ text/html 2018-04-20T16:55:28-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:etov?rev=1524268528 Consider the electric field $\vec{E} = \alpha\left( \frac{3\cos\theta}{r^4}\hat{r} + \frac{\sin\theta}{r^4}\hat{\theta}\right)$. text/html 2018-04-20T16:55:28-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:etova?rev=1524268528 Find the electric potential. In addition to your usual sense-making, include a reasonable graph. text/html 2018-04-20T16:55:28-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:etovb?rev=1524268528 Find the charge density. In addition to your usual sense-making, include a reasonable graph. text/html 2015-10-01T11:38:26-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:etoz?rev=1443724706 Use \textsl{Mathematica} to plot the real and imaginary parts of $e^z$ for $z=x+iy$, $x$ and $y$ real. text/html 2015-09-27T17:09:28-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:euler?rev=1443398968 Use Euler's formula $e^{i\theta}=\cos\theta+i\sin\theta$ and its complex conjugate to find formulas for $\sin\theta$ and $\cos\theta$. In your physics career, you will often need to read these formula ``backwards,'' i.e. notice one of these combinations of exponentials in a sea of other symbols and say, ``Ah ha! that is $\cos\theta$.'' So, pay attention to the result of the homework problem! text/html 2015-09-27T17:09:28-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:expformpractice?rev=1443398968 For each of the following complex numbers $z$, find $z^2$, $\vert z\vert^2$, and rewrite $z$ in exponential form, i.e. as a magnitude times a complex exponential phase: \begin{description} \item $z_1=i$, \item $z_2=2+2i$, \item $z_3=3-4i$. \end{description} text/html 2015-09-23T18:12:15-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:factorexp?rev=1443057135 Express $e^{i\omega t/2}-e^{-i3\omega t/2}$ in rectangular ($x+iy$) and exponential ($re^{i\theta}$) forms. ($\omega t$ is real \& $\sin(\omega t)>0$) text/html 2009-09-22T09:20:47-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:finitediska?rev=1253636447 Starting with the integral expression for the electrostatic potential due to a ring of charge, find the value of the potential everywhere along the axis of symmetry. text/html 2009-09-22T09:20:47-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:finitediskb?rev=1253636447 Find the electrostatic potential everywhere along the axis of symmetry due to a finite disk of charge with uniform (surface) charge density $\sigma$. Start with your answer to part (a) text/html 2009-09-22T09:20:47-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:finitediskc?rev=1253636447 Find two nonzero terms in a series expansion of your answer to part (b) for the value of the potential very far away from the disk. text/html 2013-10-29T20:12:27-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:fluxcube?rev=1383102747 A charge $q$ sits at the corner of a cube. Find the flux of $\EE$ through each side of the cube. Do not do a long calculation (either by hand or by computer)! text/html 2011-02-22T11:24:02-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:fluxcylinder?rev=1298402642 What do you think will be the flux through the cylindrical surface that is placed as shown in the constant vector field in the figure on the left? What if the cylinder is placed upright, as shown in the figure on the right? Explain. [Figure: first cylinder] [Figure: second cylinder] text/html 2019-04-21T22:13:33-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:fluxparaboloid?rev=1555910013 Find the upward pointing flux of the electric field $\Vec E =E_0\, z\, \hat z$ through the part of the surface $z=-3 r^2 +12$ (cylindrical coordinates) that sits above the $(x, y)$--plane. text/html 2018-04-20T16:55:28-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:gausslaw?rev=1524268528 A positively charged dielectric cylindrical shell of inner radius $a$ and outer radius $b$ has a cylindrically symmetric internal charge density $$\rho = 3\,\alpha \; \sin\left(\frac{\pi(s-a)}{b-a}\right)$$ where $\alpha$ is a constant with appropriate dimensions. text/html 2009-11-11T09:05:37-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:gausslawa?rev=1257959137 Sketch the charge density and find the total charge on the shell. text/html 2009-09-30T11:28:48-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:gausslawb?rev=1254335328 Write the volume charge density everywhere in space as a single function. text/html 2018-04-20T16:55:28-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:gausslawc?rev=1524268528 Use Gauss's Law and symmetry arguments to find the electric field in each of the regions given below: (i) $s < a$ (ii) $a < s < b$ (iii) $s > b$ text/html 2018-04-20T16:55:28-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:gausslawd?rev=1524268528 Sketch the $s$-component of the electric field as a function of $s$. text/html 2019-04-26T17:06:52-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:gausslawdifferential?rev=1556323612 For an infinitesimally thin cylindrical shell of radius $b$ with uniform surface charge density $\sigma$, the electric field is zero for $s<b$ and $\vec{E}= \frac{\sigma b}{\epsilon_0 s}\, \hat s$ for $s > b$. Use Gauss' Law to find the charge density everywhere in space. text/html 2018-04-20T16:55:28-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:gausslawlimit?rev=1524268528 Referring to the charge distribution in the Gauss's Law problem which you have solved above, take the limit as $a\to b$ so that the shell becomes infinitely thin, but keeping the total charge on a unit length of the cylinder constant. Redo each part of the previous problem for this situation. text/html 2012-10-26T18:10:50-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:gausslawlimita?rev=1351300250 Find the surface charge density on the shell. text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:gausslawlimitb?rev=1350110878 Write the volume charge density everywhere in space as a single function. Be careful: Integrate your charge density to get the total charge as a check. text/html 2018-04-20T16:55:28-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:gausslawlimitc?rev=1524268528 Use Gauss's Law and symmetry arguments to find the electric field at each region given below: (i) $s < b$ (ii) $s > b$ text/html 2009-09-30T11:28:48-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:gausslawlimitchallenge?rev=1254335328 Take the limits of the shell in the previous problem as $a\to b$ and then $b\to0$, so that the shell becomes a charged line, but keeping the total charge on a unit length of the cylinder constant. text/html 2009-09-30T11:28:48-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:gausslawlimitchallengea?rev=1254335328 Find the charge density on the line. text/html 2009-09-30T11:28:48-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:gausslawlimitchallengeb?rev=1254335328 Give a formula for the charge density everywhere in space. Be careful: Integrate your charge density to get the total charge as a check. text/html 2009-09-30T11:28:48-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:gausslawlimitchallengec?rev=1254335328 Use Gauss's Law and symmetry arguments to find the electric field for $r>0$. text/html 2018-04-20T16:55:28-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:gausslawlimitd?rev=1524268528 Sketch the $s$-component of the electric field as a function of $s$. text/html 2018-04-20T16:55:28-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:gausslawlimite?rev=1524268528 Compare the surface charge density on the shell to the discontinuity in the $s$-component of the electric field. text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:gausslawsymmetry?rev=1350110878 %Adapted from Colorado Clicker Questions 4 and 5 Below are 4 surfaces (I, II, III, and IV) that are coaxial with an infinitely long line of charge with uniform charge density $\lambda$.\\ For this problem, explanations will count for the majority of the points. text/html 2015-10-16T14:31:48-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:gausslawsymmetrya?rev=1445031108 Which of these surfaces have $\Phi_E=\frac{\lambda L}{\epsilon_0}$? How do you know? text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:gausslawsymmetryb?rev=1350110878 For which of these Gaussian surfaces will Gauss' Law in help us to calculate $\vec{E}$ at point $P$ due to the line of charge. (Point $P$ is at the top center of each Gaussian surface)? How do you know? text/html 2014-10-16T09:06:31-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:graddivcurldescription?rev=1413475591 What comes to mind when you think about divergence? Write down everything you know which includes various notations, formulas, properties, definitions, representations, and physics examples. text/html 2014-10-10T16:05:42-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:gradientpractice?rev=1412982342 Find the gradient of each of the following functions: text/html 2014-10-10T16:05:42-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:gradientpracticea?rev=1412982342 $$f(x,y,z)=e^{(x+y)}+x^2 y^3 \ln \frac{x}{z}$$ text/html 2014-10-10T16:05:42-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:gradientpracticeb?rev=1412982342 $$\sigma(\theta,\phi)=\cos\theta \sin^2\phi$$ text/html 2014-10-10T16:05:42-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:gradientpracticec?rev=1412982342 $$\rho(s,\phi,z)=(s+3z)^2\cos\phi$$ text/html 2012-09-23T14:04:57-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:gradientptcharge?rev=1348434297 Consider the fields at a point $\rr$ due to a point charge located at $\rr'$. text/html 2011-11-22T18:33:12-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:gradientptchargea?rev=1322015592 Write down an expression for the electrostatic potential $V(\rr)$ at a point $\rr$ due to a point charge located at $\rr'$. (There is nothing to calculate here.) text/html 2011-11-22T18:33:12-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:gradientptchargeb?rev=1322015592 Write down an expression for the electric field $\EE(\rr)$ at a point $\rr$ due to a point charge located at~$\rr'$. (There is nothing to calculate here.) text/html 2011-11-22T18:33:12-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:gradientptchargec?rev=1322015592 Working in rectangular coordinates, compute the gradient of $V$. text/html 2009-08-21T17:29:03-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:gradientptcharged?rev=1250900943 Write several sentences comparing your answers to the last two questions. text/html 2014-10-10T16:05:42-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:gradientptchargeorigin?rev=1412982342 The electrostatic potential due to a point charge at the origin is given by: $$V=\frac{1}{4\pi\epsilon_0} \frac{q}{r}$$ text/html 2014-10-10T16:05:42-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:gradientptchargeorigina?rev=1412982342 Find the electric field due to a point charge at the origin as a gradient in rectangular coordinates. text/html 2014-10-10T16:05:42-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:gradientptchargeoriginb?rev=1412982342 Find the electric field due to a point charge at the origin as a gradient in spherical coordinates. text/html 2014-10-10T16:05:42-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:gradientptchargeoriginc?rev=1412982342 Find the electric field due to a point charge at the origin as a gradient in cylindrical coordinates. text/html 2010-11-07T05:24:09-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:helix?rev=1289136249 A helix with 17 turns has height $H$ and radius $R$. Charge is distributed on the helix so that the charge density increases like the square of the distance up the helix. At the bottom of the helix the linear charge density is $0~{\hbox{C}\over\hbox{m}}$. At the top of the helix, the linear charge density is $13~{\hbox{C}\over\hbox{m}}$. What is the total charge on the helix? text/html 2009-08-21T07:20:50-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:icecreammass?rev=1250864450 Use integration to find the total mass of ice cream in a packed cone (both cone and hemisphere of ice cream on top). text/html 2009-09-22T09:20:47-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:infinitedisk?rev=1253636447 Find the electrostatic potential due to an infinite disk, using your results from the finite disk problem. text/html 2016-08-25T16:41:34-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:integrategravpotential?rev=1472168494 The change in gravitational potential energy can be found by integrating $$\Delta U=\int_{r_i}^{r_f}{G\frac{m_1m_2}{r^2}dr}$$ where $G$ is the gravitational constant, $m_1$ and $m_2$ are masses, and $r$ is the distance between the two masses. text/html 2018-03-30T09:54:38-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:integrategravpotentiala?rev=1522428878 Perform the integration, showing all steps. text/html 2014-09-20T13:50:43-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:integrategravpotentialb?rev=1411246243 Plot the potential energy, $\Delta U$, as the mass, $m_1$, varies. Label significant points on the plot and describe (in words) the behavior. text/html 2014-09-20T13:50:43-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:integrategravpotentialc?rev=1411246243 Plot the potential energy, $\Delta U$, as the final distance, $r_f$, varies. Label significant points on the plot and describe the behavior. text/html 2018-05-02T17:18:45-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:laplace?rev=1525306725 Consider the bounded two-dimensional region from class. Three sides are metal and held at $V = 0$ while one is an insulator on which the potential is known to be: $V(x, b) = V_0\left(\sin\left(\frac{\pi x}{a}\right) + \sin\left(\frac{2\pi x}{a}\right) - \sin\left(\frac{3\pi x}{a}\right) \right)$ text/html 2018-05-02T17:18:45-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:laplacea?rev=1525306725 Starting from the general solution from the practice problem, find a symbolic expression for the potential $V(x, y)$. text/html 2018-05-02T17:18:45-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:laplaceb?rev=1525306725 Make several plots of your solution and discuss any interesting features you find. (I particularly recommend both surface plots and plots of $x$- and $y$-cross sections at several different values.) text/html 2018-05-02T17:18:45-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:laplacec?rev=1525306725 Suppose that the fourth side of the region is also a conductor at constant potential $V_0$. Find a symbolic expression for $V(x, y)$, graph your solution, and discuss its features. text/html 2018-05-02T17:18:45-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:laplacepractice?rev=1525306725 Laplace's equation in two dimensions is: $\frac{\partial^2 V}{\partial x^2} + \frac{\partial^2 V}{\partial y^2} = 0$. Assume the region if interest is a rectangle of width $a$ and height $b$. text/html 2018-05-02T17:18:45-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:laplacepracticea?rev=1525306725 Use separation of variables to find the general solution to Laplace's equation in two dimensions. text/html 2018-05-02T17:18:45-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:laplacepracticeb?rev=1525306725 Suppose three of the boundaries ($x=0$, $x=a$, and $y=0$) are known to have $V=0$. Find the general solution in this case. text/html 2018-05-02T17:18:45-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:laplacepracticec?rev=1525306725 Suppose only one boundary ($y=0$) is known to have $V=0$, and that two boundaries ($x=0$ and $x=a$) are known to have $\frac{\partial V}{\partial x} = 0$. Find the general solution in this case. text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:linesources?rev=1350110878 Consider the fields around both finite and infinite uniformly charged, straight wires. text/html 2011-11-22T18:33:12-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:linesourcesa?rev=1322015592 Find the electric field around an infinite, uniformly charged, straight wire, starting from the expression for the electrostatic potential that we found in class: $$V(\Vec r)={2\lambda\over 4\pi\epsilon_0}\, \ln{ r_0\over r}$$ Compare your result to the solution found from Coulomb's law. Which method is easier? text/html 2011-11-22T18:33:12-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:linesourcesb?rev=1322015592 Find the electric field around a finite, uniformly charged, straight wire, at a point a distance $r$ straight out from the midpoint, starting from the expression for the electrostatic potential that we found in class: $$V(\Vec r)={\lambda\over 4\pi\epsilon_0} \left[\ln{\left(L + \sqrt{L^2+r^2}\right)}- \ln{\left(-L + \sqrt{L^2+r^2}\right)}\right]$$ text/html 2009-08-22T08:26:57-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:linesourcesc?rev=1250954817 Find the electric field around an infinite, uniformly charged, straight wire, starting from Coulomb's Law. text/html 2019-04-21T22:13:33-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:linesourcesd?rev=1555910013 Find the electric field around a finite, uniformly charged, straight wire, at a point a distance $s$ straight out from the midpoint, starting from Coulomb's Law. text/html 2014-10-10T16:05:42-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:linesourcesgradonlya?rev=1412982342 Find the electric field around an infinite, uniformly charged, straight wire, starting from the following expression for the electrostatic potential: $$V(\Vec r)={2\lambda\over 4\pi\epsilon_0}\, \ln{ s_0\over s}$$ %Compare your result to the solution found from Coulomb's law. Which method is easier? text/html 2018-03-30T09:56:07-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:mathematicaintegrals?rev=1522428967 Use Mathematica to find the following integrals. \begin{eqnarray*} I_1&=&\int_0^{\sqrt{2\pi}}\sin\left(x^2\right)dx\\ I_2&=&\int_{-1}^1\int_0^{1-x^2}{\sin\left(xy\right)dy}dx\\ I_3&=&\int\sinh\left(kx\right)dx\\ I_4&=&\int_0^{2\pi}\frac{dx}{\sqrt{1-A\cos\left(x\right)}}\\ \end{eqnarray*} text/html 2018-03-30T09:54:38-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:mathematicaplot?rev=1522428878 Use Mathematica to plot (and print out) each of the following functions: \begin{eqnarray*} f_1(x)&=&\sin\left(x^3\right)\\ f_2(x)&=&\frac{e^x}{x^3}\\ f_3(x,y)&=&\sinh\left(y\right)\\ f_4(x,y)&=&\sin\left(x+y\right)^3 \end{eqnarray*} Make sure you use best practices for creating plots: all plots should have a title, labeled axes (with units, when appropriate), and a domain and range that include the interesting behaviors of the function. text/html 2018-03-30T09:54:38-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:mathematicapractice?rev=1522428878 If you are unfamiliar with Mathematica and you have not already done so, go through the following tutorials: <http://www.wolfram.com/broadcast/screencasts/handsonstart/> More detailed information can be found at: <http://www.wolfram.com/support/learn/> text/html 2019-04-05T17:13:18-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:moremathematica?rev=1554509598 Use Mathematica to make a contour plot of the electric potential in the $xy$-plane due to a single point charge located at the origin. Make sure to label your plot in a sensible way, including indicating the values you used for any unknown parameters (make sure you choose reasonable values). text/html 2009-09-21T21:33:08-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:multipole?rev=1253593988 Find the distance $\left\vert\rr -\rr'\right\vert$ between the point $\rr$ and the point $\rr'$ in terms of the magnitudes of $\rr$ and $\rr'$ and $\gamma$, the angle between them. (Do not choose a coordinate system.) Then assuming that $\rr>>\rr'$, find a series expansion for $\left\vert\rr -\rr'\right\vert$, correct to fourth order. This expansion is the basis of multipole expansions, used in both electromagnetic theory and quantum mechanics. text/html 2019-04-21T22:13:33-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:murdermystery?rev=1555910013 (Throughout this problem, assume all of the constants-including invisible factors of 1-carry the necessary dimensions so that the fields in this problem are dimensionally correct.) Consider the vector field in rectangular coordinates: $$\vec{E} = \frac{q}{4 \pi \epsilon_{0}} [(2 x y^3z+z)\hat{x} + (3x^2 y^2 z) \hat{y}+(x^2 y^3+x)\hat{z}]$$ text/html 2018-04-20T16:55:28-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:murdermysterya?rev=1524268528 Using only the $x$-component of $\vec{E}$, find as much information as possible about the potential from which this electric field might have come. text/html 2018-04-20T16:55:28-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:murdermysteryb?rev=1524268528 Repeat this exercise for the $y$- and $z$-components of $\vec{E}$. Does this field come from a potential? text/html 2018-04-20T16:55:28-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:murdermysteryc?rev=1524268528 Consider the different vector field: $$\vec{E} = \frac{q}{4 \pi \epsilon_{0}} (-y \hat{x} + x \hat{y})$$ Does this field come from a potential? text/html 2018-04-20T16:55:28-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:murdermysteryd?rev=1524268528 Consider the different vector field: $$\vec{E}=\frac{q}{4 \pi \epsilon_{0}} \left(s \hat{\phi}\right)$$ Does this field come from a potential? text/html 1969-12-31T16:00:00-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:nonuniformdiskQE?rev= text/html 1969-12-31T16:00:00-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:nonuniformdiskQEa?rev= text/html 1969-12-31T16:00:00-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:nonuniformdiskQEb?rev= text/html 2014-10-01T17:53:19-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:onions?rev=1412211199 Find the derivative of the following functions (and make sure that you can do similar problems with different combinations of the common transcendental functions): \begin{eqnarray*} f(x)&=&\sin\left(x^3\right)\\ f(x)&=&\frac{e^x}{x^3} \end{eqnarray*} text/html 2019-04-21T22:13:33-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:pathindependence?rev=1555910013 The gravitational field due to a spherical shell of mass is given by: %/* \[ \Vec g =\begin{cases} 0&r<b\\ -\frac{4}{3}\pi\rho\,G\left({r}-{b^3\over r^2}\right)\hat{r}&b<r<a\\ -\frac{4}{3}\pi\rho\, G\left({a^3-b^3\over r^2}\right)\hat{r}&a<r\\ \end{cases} \] text/html 2012-10-31T17:31:12-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:pathindependencea?rev=1351729872 Using an explicit line integral, calculate the work required to bring a test mass, of mass $m_0$, from infinity to a point $P$, which is a distance $c$ (where $c>a$) from the center of the shell. [Figure: integration paths for parts a), b), and c)] text/html 2009-10-01T21:06:22-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:pathindependenceb?rev=1254456382 Using an explicit line integral, calculate the work required to bring the test mass along the same path, from infinity to the point $Q$ a distance $d$ (where $b<d<a$) from the center of the shell. text/html 2009-10-01T21:06:22-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:pathindependencec?rev=1254456382 Using an explicit line integral, calculate the work required to bring the test mass along the same radial path from infinity all the way to the center of the shell. text/html 2012-10-31T17:31:12-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:pathindependenced?rev=1351729872 Using an explicit line integral, calculate the work required to bring in the test mass along the path drawn below, to the point $P$ of question a. Compare the work to your answer from question a. [Figure: integration path for parts d)] text/html 2012-10-31T17:31:12-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:pathindependencee?rev=1351729872 What is the work required to bring the test mass from infinity along the path drawn below to the point $P$ of question a. Explain your reasoning. [Figure: integration paths for part e)] text/html 2014-09-20T13:50:43-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:pdm1d?rev=1411246243 From your data collected in class using the ``Derivative Machine”, calculate the internal energy at five points. Show calculations and draw a graphical representation of the data. Include a brief discussion (using strong scientific writing) on the chosen step size in your data and the dependency of your variables. Briefly describe another procedure which could be used to measure the same integral with your machine. text/html 2014-10-01T17:53:19-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:pdm1dderivlab?rev=1412211199 For the data you collected from the derivatives machine, write a short but clear report finding the derivative $$\frac{dx}{dF}$$ Decide for yourself what sections you need in your report. At a minimum, include a clear statement of the problem you are trying to solve, a description of how you collected your data, the data itself, a clear description of how you analyzed the data, and a clear statement of what you can conclude from your analysis. Use a combination of words interlaced with other… text/html 2016-08-25T13:33:07-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:pdm1dintlab?rev=1472157187 For the data you collected from the integration machine, or you can use our data listed below, write a short but clear report finding the potential energy stored in the machine. Decide for yourself what sections you need in your report. At a minimum, include a clear statement of the problem you are trying to solve, a description of the apparatus, a description of how you collected your data, the data itself, a clear description of how you analyzed the data, and a clear statement of what you c… text/html 2011-11-22T18:33:12-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:potentialconegem227?rev=1322015592 A conical surface (an empty ice-cream cone) carries a uniform charge density $\sigma$. The height of the cone is $a$, as is the radius of the top. Find the potential at point $P$ (in the center of the opening of the cone), letting the potential at infinity be zero. text/html 2009-08-19T15:35:04-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:potentialvsenergy?rev=1250721304 In this course, two of the primary examples we will be using are the force due to gravity and the force due to an electric charge. Both of these forces vary like $1/r^2$, so they will have many, many similarities. Most of the calculations we do for the one case will be true for the other. But there are some extremely important differences: text/html 2009-08-19T15:35:04-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:potentialvsenergya?rev=1250721304 Find the value of the electric potential energy of a system consisting of a hydrogen nucleus and an electron separated by the Bohr radius. Find the value of the gravitational potential energy of the same two particles at the same radius. Use the same system of units in both cases. Compare and the contrast the two answers. text/html 2009-08-19T15:35:04-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:potentialvsenergyb?rev=1250721304 Find the value of the electric potential due to the nucleus of a hydrogen atom at the Bohr radius. Find the gravitational potential due to the nucleus at the same radius. Use the same system of units in both cases. Compare and contrast the two answers. text/html 2009-08-19T15:35:04-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:potentialvsenergyc?rev=1250721304 Think of and briefly discuss at least one other fundamental difference between electromagnetic and gravitational systems. Hint: Why are we bound to the earth gravitationally, but not electromagnetically? text/html 2009-08-20T14:50:36-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:quadrupole?rev=1250805036 Consider a series of three charges arranged in a line along the $z$-axis, charges $+Q$ at $z=\pm D$ and charge $-2Q$ at $z=0$. text/html 2019-04-10T20:38:12-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:quadrupolea?rev=1554953892 Find the electrostatic potential at a point $P$ in the $xy$-plane at a distance $s$ from the center of the quadrupole. text/html 2019-04-10T20:38:12-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:quadrupoleb?rev=1554953892 Assume $s>>D$. Find the first two non-zero terms of a power series expansion to the electrostatic potential you found in the first part of this problem. text/html 2009-08-20T14:50:36-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:quadrupolec?rev=1250805036 Is it possible to find the electric field at $P$ from your answer to the first part of the problem? If you answered that it is possible, find the electric field. If you answered that it is not possible, explain your answer. text/html 2009-08-20T14:50:36-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:quadrupoled?rev=1250805036 A series of charges arranged in this way is called a linear quadrupole. Why? text/html 2015-09-28T16:09:01-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:quizangle?rev=1443481741 Find the location of the point in both rectangular and polar coordinates. (Similarly be able to find the sine and cosine of any angle which is a multiple of $\frac{\pi}{4}$ or $\frac{\pi}{6}$). \begin{tikzpicture} \begin{axis}[width=3.5in, xtick={-2,-1,...,1}, ytick={-1,0,...,2}, text/html 2019-04-13T08:58:46-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:quizarea?rev=1555171126 Find the area element $dA$ on a surface of high symmetry such as the top or side of a cylinder or the curved or flat surface of a hemisphere. text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:quizcrossproduct?rev=1350110878 Are the following equalities true or false? Why? text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:quizcrossproducta?rev=1350110878 \begin{equation*} \hat{y} \cdot \hat{z}=\hat{x} \end{equation*} text/html 2020-01-24T19:13:42-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:quizcrossproductb?rev=1579922022 \begin{equation*} \hat{r}_{\text{cyl}} \times \hat{z}=-\hat{\phi} \end{equation*} text/html 2020-01-24T19:13:42-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:quizcrossproductc?rev=1579922022 \begin{equation*} \hat{r}_{\text{sph}} \times \hat{\phi}=\hat{\theta} \end{equation*} text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:quizcrossproductd?rev=1350110878 \begin{equation*} \hat{r}\cdot \hat{\theta}=1 \end{equation*} text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:quizdel?rev=1350110878 Which of the following are valid operations? How do you know? text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:quizdela?rev=1350110878 \begin{equation*} \vec{\nabla}\cdot\left(\vec{\nabla}F\right) \end{equation*} text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:quizdelb?rev=1350110878 \begin{equation*} \vec{\nabla}\left(\vec{\nabla}\times \vec{F}\right) \end{equation*} text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:quizdelc?rev=1350110878 \begin{equation*} \vec{\nabla}\times \left(\vec{\nabla}\cdot \vec{F}\right) \end{equation*} text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:quizdeld?rev=1350110878 \begin{equation*} \vec{\nabla}\cdot\left(\vec{\nabla}\times \vec{F}\right) \end{equation*} text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:quizdele?rev=1350110878 \begin{equation*} \vec{\nabla}\times \left(\vec{\nabla}\times \vec{F}\right) \end{equation*} text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:quizdelta?rev=1350110878 Are the following equalities true or false? Why? text/html 2014-09-20T12:30:40-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:quizdeltaa?rev=1411241440 $\frac{d}{dx} \Theta(x-a)=\delta(x-a)$ text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:quizdeltab?rev=1350110878 \begin{equation*} \int_{-\infty}^{+\infty}\delta(x)\,dx=0 \end{equation*} text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:quizdeltac?rev=1350110878 \begin{equation*} x\,\delta(x)=0 \end{equation*} text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:quizdeltad?rev=1350110878 \begin{equation*} \Theta(x-a)=\int_{-\infty}^{x}\delta(u-a)\,du \end{equation*}\\ text/html 2012-10-26T18:10:50-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:quizdifferential?rev=1351300250 Find the total differential $df$ for each of the following functions. text/html 2012-10-26T18:10:06-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:quizdifferentiala?rev=1351300206 \begin{equation*} f=xyz \end{equation*} text/html 2012-10-26T18:10:06-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:quizdifferentialb?rev=1351300206 \begin{equation*} f=\sqrt{x^2+y^2+z^2} \end{equation*} text/html 2012-10-26T18:10:06-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:quizdifferentialc?rev=1351300206 \begin{equation*} f=r\,\tan(2\theta) \end{equation*} text/html 2012-10-26T18:10:06-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:quizdifferentiald?rev=1351300206 \begin{equation*} f=z\,e^{(x^2+y^2)/a^2} \end{equation*} text/html 2012-10-26T18:10:06-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:quizdifferentiale?rev=1351300206 \begin{equation*} f=Nk\ln\left[\frac{(V-Nb)T^{3/2}}{N\Phi}\right]+\frac{5}{2}Nk \end{equation*} text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:quizdotproduct?rev=1350110878 Are the following equalities true or false? Why? text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:quizdotproducta?rev=1350110878 \begin{equation*} \left(\hat{x}-\hat{z} \right)\cdot \hat{x}=-1 \end{equation*} text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:quizdotproductb?rev=1350110878 \begin{equation*} \left(\hat{x}-\hat{z} \right)\times \hat{x}=-\hat{y} \end{equation*} text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:quizdotproductc?rev=1350110878 \begin{equation*} \left(\hat{x}+\hat{y} \right)\cdot \hat{z}=0 \end{equation*} text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:quizdotproductd?rev=1350110878 \begin{equation*} \left(\hat{x}+\hat{y} \right)\times \hat{z}=\hat{x}+\hat{y} \end{equation*} text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:quizdr?rev=1350110878 Write $\vec{dr}$ in rectangular, cylindrical, and spherical coordinates. \begin{enumerate} \item Rectangular: $\vec{dr}=$\\ \item Cylindrical: $\vec{dr}=$\\ \item Spherical: $\vec{dr}=$\\ \end{enumerate} text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:quizintegrals?rev=1350110878 Evaluate the following indefinite integrals. text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:quizintegralsa?rev=1350110878 \begin{equation*} \int \sin(x)\, dx \end{equation*} text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:quizintegralsb?rev=1350110878 \begin{equation*} \int \frac{1}{x}\, dx \end{equation*} text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:quizintegralsc?rev=1350110878 \begin{equation*} \int e^{kx}\, dx \end{equation*} text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:quizintegralsd?rev=1350110878 \begin{equation*} \int \left(x^2+\frac{y}{x^2}\right)\, dx \end{equation*}\\ text/html 2012-10-26T18:10:06-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:quizpotential?rev=1351300206 You have a charge distribution composed of two point charges along the $z$-axis: one with charge $+3q$ located at $z=-a$ and the other with charge $-q$ located at $z=+b$. Write down the electrostatic potential at every point in space due to these two charges in rectangular, cylindrical, and spherical coordinates. text/html 2012-10-26T18:10:06-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:quizpotentiala?rev=1351300206 Rectangular: $V(\vec{r})=$\\ text/html 2012-10-26T18:10:06-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:quizpotentialb?rev=1351300206 Cylindrical: $V(\vec{r})=$\\ text/html 2012-10-26T18:10:06-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:quizpotentialc?rev=1351300206 Spherical: $V(\vec{r})=$\\ text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:quizproductrules?rev=1350110878 Are the following equalities true or false? Why? text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:quizproductrulesa?rev=1350110878 \begin{equation*} \hat{y} \times \hat{z}=\hat{x} \end{equation*} text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:quizproductrulesb?rev=1350110878 \begin{equation*} \hat{y} \times \hat{z}=\hat{x} \end{equation*} text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:quizproductrulesc?rev=1350110878 \begin{equation*} \hat{y} \times \hat{z}=\hat{x} \end{equation*} text/html 2016-08-25T16:44:39-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:quizseriesmemorize?rev=1472168679 Be able to give the first four nonzero terms of the power series for $\sin z$, $\cos z$, $e^z$, $\ln(1+z)$, and $(1+z)^p$. text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:quizusewhatyouknow?rev=1350110878 What is $\vec{dr}$ along the path $y=x^3$? text/html 2019-04-13T08:58:46-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:quizvolume?rev=1555171126 Write the volume element $d\tau$ in rectangular, cylindrical, and spherical coordinates. \begin{enumerate} \item Rectangular: $d\tau=$\\ \item Cylindrical: $d\tau=$\\ \item Spherical: $d\tau=$\\ \end{enumerate} text/html 2011-11-22T18:33:12-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:remember?rev=1322015592 Briefly describe in words something you learned from doing this problem that you would like to remember for the future. Make your statement using good scientific writing, as you would in a research paper. text/html 2011-12-06T10:17:51-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:repulsionns?rev=1323195471 A metal sphere of radius $R$ carries a total charge $Q$. What is the force of repulsion between the ``northern” hemisphere and the ``southern” hemisphere? text/html 2011-10-16T20:18:41-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:sensemaking?rev=1318821521 Use some form of sensemaking to evaluate your answer, e.g.\ check the units or dimensions, check the size of your answer, check a limiting case, compare to other known cases, etc. text/html 2020-01-22T09:21:18-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:seriesconvergence?rev=1579713678 Recall that, if you take an infinite number of terms, the series for $\sin z$ and the function itself $f(z)=\sin z$ are equivalent representations of the same thing for all real numbers $z$, (in fact, for all complex numbers $z$). This is not always true. More commonly, a series is only a valid, equivalent representation of a function for some more restricted values of $z$. The technical name for this idea is convergence--the series only “converges” to the value of the function on some res… text/html 1969-12-31T16:00:00-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:seriesconvergenceMaple?rev= text/html 2009-08-19T21:30:41-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:seriesnotation1?rev=1250742641 Write out the first four nonzero terms in the series: text/html 2009-08-19T21:30:41-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:seriesnotation1a?rev=1250742641 $$\sum\limits_{n=0}^\infty {1\over n!}$$ text/html 2009-08-19T21:30:41-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:seriesnotation1b?rev=1250742641 $$\sum\limits_{n=1}^\infty {(-1)^n\over n!}$$ text/html 2009-08-19T21:30:41-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:seriesnotation2?rev=1250742641 Write the following series using sigma $\left(\sum\right)$ notation. text/html 2009-08-19T21:30:41-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:seriesnotation2a?rev=1250742641 $$1 - 2\,\theta^2 + 4\,\theta^4 - 8\,\theta^6 +\,\dots$$ text/html 2009-08-19T21:30:41-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:seriesnotation2b?rev=1250742641 $${1\over4} - {1\over9} + {1\over16} - {1\over 25}+\,\dots$$ text/html 2009-08-19T21:30:41-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:seriesnotation3?rev=1250742641 If you need more practice with sigma $\left(\sum\right)$ notation, you can get really good practice by going back and forth between the two representations of the standard power series on the memorization page. Power series are used everywhere in physics and it is very important to be able to translate back and forth between the two representations. text/html 2009-09-30T08:49:24-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:slabmass?rev=1254325764 Determine the total mass of each of the slabs below. text/html 2009-09-30T08:49:24-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:slabmassa?rev=1254325764 A square slab of side length $L$ with thickness $h$, resting on a table top at $z=0$, whose mass density is given by $\rho=A\pi\sin(\pi z/h)$. text/html 2009-09-30T08:49:24-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:slabmassb?rev=1254325764 A square slab of side length $L$ with thickness $h$, resting on a table top at $z=0$, whose mass density is given by \begin{equation} \rho = 2A \Big( \Theta(z)-\Theta(z-h) \Big) \end{equation} text/html 2009-09-30T08:49:24-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:slabmassc?rev=1254325764 An infinitesimally thin square sheet of side length $L$, resting on a table top at $z=0$, whose surface density is given by $\sigma=2Ah$. text/html 2009-09-30T08:49:24-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:slabmassd?rev=1254325764 An infinitesimally thin square sheet of side length $L$, resting on a table top at $z=0$, whose mass density is given by $\rho=2Ah\,\delta(z)$. text/html 2011-10-25T16:55:50-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:slabmasse?rev=1319586950 What are the dimensions of $A$? text/html 2011-10-25T16:55:50-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:slabmassf?rev=1319586950 Write several sentences comparing your answers to the different cases above. text/html 2018-05-02T17:18:45-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:squarehoopgem24?rev=1525306725 Consider a square loop with each side length $a$ carrying a uniform linear charge density $\lambda$. text/html 2009-08-22T08:57:21-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:squarehoopgem24a?rev=1250956641 Find the electric field a distance $z$ above the center of the square. (You may start with the electric field due to a single finite line of charge). text/html 2009-08-22T08:57:21-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:squarehoopgem24b?rev=1250956641 Find the work needed to bring a charge in from infinity along the $z$-axis. text/html 2018-05-02T17:18:45-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:squarehoopgem24c?rev=1525306725 Use two different methods to find the value of the electric potential a distance $z$ above the center of the square. text/html 2018-05-21T11:06:57-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:stokes?rev=1526926017 In this problem, you will be investigating, from several different points of view, a cylindrical wire of finite thickness $R$, carrying a non-uniform current density $J=\kappa s$, where $\kappa$ is a constant and $s$ is the distance from the axis of the cylinder.\\ text/html 2012-10-31T17:31:12-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:stokesa?rev=1351729872 Find the total current flowing through the wire.\\ text/html 2012-10-31T17:31:12-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:stokesb?rev=1351729872 Find the current flowing through Disk 2, a central (circular cross-section) portion of the wire out to a radius $r_2<R$.\\ [Figure: cross section of wire] text/html 2012-10-31T17:31:12-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:stokesc?rev=1351729872 Use Amp\`ere's law in integral form to find the magnetic field at a distance $r_1$ outside the wire.\\ text/html 2012-10-31T17:31:12-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:stokesd?rev=1351729872 Use Amp\`ere's law in integral form to find the magnetic field at a distance $r_2$ inside the wire.\\ text/html 2012-10-31T17:31:12-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:stokese?rev=1351729872 Use theta functions to write the magnetic field everywhere (both inside and outside of the wire) as a single function.\\ text/html 2012-10-31T17:31:12-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:stokesf?rev=1351729872 Evaluate $$\int \left(\grad\times\BB\right)\cdot d\AA$$ for Disk 2, a circular disk of radius $r_2<R$. Use this result and part (d) to verify Stokes' theorem on this surface.\\ text/html 2012-10-31T17:31:12-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:stokesg?rev=1351729872 Evaluate $$\int \left(\grad\times\BB\right)\cdot d\AA$$ for Disk 1, a circular disk of radius $r_1>R$. Use this result and part c) to verify Stokes' theorem on this surface.\\ text/html 2012-10-12T23:47:58-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:stokesverify?rev=1350110878 Verify Stokes' Theorem for $\FF( r, \theta, \phi)=e^{r^2} \hat{r} + {1\over 2}\sin\theta \,\hat{\phi}$ where the butterfly net surface is the hemisphere of radius 5 centered at the origin with $z\ge 0$. text/html 2013-05-09T13:02:00-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:symmetry?rev=1368129720 For each of the following situations, can you use Gauss' Law to find the electric field at an arbitrary point, $P$, located outside of the charge distribution? \begin{itemize} \item If no, explain why not. \item If yes, \begin{itemize} \item draw the Gaussian surface you would use and describe why you chose that shape and orientation (\emph{i.e.} make explicit symmetry arguments), and \item use Gauss' Law to find the electric field at point $P$. \end{itemize} \end{itemize} text/html 2013-05-09T13:02:00-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:symmetrya?rev=1368129720 A charged, insulating sphere of radius, $R$, with charge density $\rho (\vec{r})=C\,\sin\theta$. \medskip \centerline{\includegraphics[scale=0.55]{\TOP Figures/vfsymmetrya}} \medskip text/html 2013-05-09T13:02:00-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:symmetryb?rev=1368129720 A neutral, infinitely long cylindrical metal shell with inner radius $a$ and outer radius $b$, with a charged wire of uniform charge density $\lambda$ at a distance $a/2$ out from the center of the cylinder, parallel to the cylinder's axis. \bigskip \centerline{\includegraphics[scale=0.55]{\TOP Figures/vfsymmetryb}} \bigskip text/html 2015-10-16T14:31:48-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:symmetryc?rev=1445031108 A charged, insulating sphere of radius $R$ with charge density $\rho (\vec{r})=\frac{C}{r^2}$. \bigskip \centerline{\includegraphics[scale=0.55]{\TOP Figures/vfsymmetryc}} \bigskip text/html 2013-05-09T13:02:00-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:symmetryd?rev=1368129720 An finite slab of width and length $L$, height $h$, and charge density $\rho(\vec{r})=C \,x^2$. \bigskip \centerline{\includegraphics[scale=0.55]{\TOP Figures/vfsymmetryd}} \bigskip text/html 2018-03-30T09:54:38-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:tetrahedron?rev=1522428878 Using a dot product, find the angle between any two line segments that join the center of a regular tetrahedron to its vertices. Hint: Think of the vertices of the tetrahedron as sitting at the vertices of a cube (at coordinates (0,0,0), (1,1,0), (1,0,1) and (0,1,1)---you may need to build a model and play with it to see how this works!) text/html 1969-12-31T16:00:00-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:thetadeltaSJP?rev= text/html 1969-12-31T16:00:00-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:thetadeltaSJPa?rev= text/html 1969-12-31T16:00:00-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:thetadeltaSJPb?rev= text/html 2009-10-01T21:28:20-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:thetaparameters?rev=1254457700 The function $\theta(x)$ (the Heaviside or unit step function) is a defined as: \begin{eqnarray*} \theta(x) = \left\{ \begin{array}{l l} 1 & \quad \mbox{for $x>0$}\\ 0 & \quad \mbox{for $x<0$}\\ \end{array} \right. \end{eqnarray*} This function is discontinuous at $x=0$ and is generally taken to have a value of $\theta(0)=1/2$. text/html 2009-08-21T07:20:50-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:totalcharge?rev=1250864450 For each case below, find the total charge. text/html 2009-08-21T07:20:50-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:totalchargea?rev=1250864450 A positively charged (dielectric) spherical shell of inner radius $a$ and outer radius $b$ with a spherically symmetric internal charge density $\rho(\rr)=\alpha\, 3e^{(kr)^3}$ text/html 2019-04-10T20:38:12-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:totalchargeb?rev=1554953892 A positively charged (dielectric) cylindrical shell of inner radius $a$ and outer radius $b$ with a cylindrically symmetric internal charge density $\rho(\rr)=\alpha\, {1\over s}\, e^{ks}$. text/html 2012-10-26T18:10:06-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:totalcurrentchallenge?rev=1351300206 For the surface current you found in Problem 1.a, find the magnetic vector potential at a distance $r$ from the center of the wire with length of $2L$. text/html 2009-10-01T21:28:20-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:totalcurrentgem55?rev=1254457700 A current $I$ flows down a wire of radius $a$. text/html 2010-10-17T09:18:54-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:totalcurrentgem55a?rev=1287332334 If it is uniformly distributed over the surface, give a formula for the surface current density $\Vec K$. text/html 2012-10-26T18:10:50-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:totalcurrentgem55b?rev=1351300250 If it is distributed in such a way that the volume current density, $|\Vec J|$, is inversely proportional to the distance from the axis, give a formula for $\Vec J$. text/html 2012-10-26T18:10:06-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:totalcurrentpracticea?rev=1351300206 Current $I$ flows down a wire (length $L$) with square cross-section (side $a$). If it is uniformly distributed over the entire area, what is the magnitudes of the volume current density $\vec{J}$? text/html 2019-04-26T17:06:52-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:totalcurrentpracticeb?rev=1556323612 If it is uniformly distributed over the outer surfaces only, what is the magnitude of the surface current density $\vec{K}$? text/html 2009-09-30T08:49:24-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:triangleparameters?rev=1254325764 Consider the function: \begin{eqnarray*} f(x) = 3x\,\theta(x)\,\theta(1-x)+(6-3x)\,\theta(x-1)\,\theta(2-x) \end{eqnarray*} Make sketches of the following functions, by hand, on the axes with the same scale and domain. Briefly describe, using good scientific writing that includes both words and equations, the role that the number two plays in the shape of each graph: \begin{eqnarray} y &=& f(x)\\ y &=& 2+f(x)\\ y &=& f(2+x)\\ y &=& 2f(x)\\ y &=& f(2x) \end{eqnarray} text/html 2009-09-30T08:49:24-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:trigparameters?rev=1254325764 Make sketches of the following functions, by hand, all on the same axes. Briefly describe, using good scientific writing that includes both words and equations, the role that the number two plays in the shape of each graph: \begin{eqnarray} y &=& \sin x\\ y &=& 2+\sin x\\ y &=& \sin(2+x)\\ y &=& 2\sin x\\ y&=& \sin 2x \end{eqnarray} text/html 2018-03-30T09:54:38-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:v4chargessquare?rev=1522428878 Four point charges sit at the corners of a square in the $xy$-plane. A positive point charge is located at $(a,a,0)$ and another is located at $(-a,a,0)$. A negative charge is located at $(-a,-a,0)$ and another is located at $(a,-a,0)$. text/html 2016-09-23T16:33:57-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:v4chargessquarea?rev=1474673637 Find the electric potential at any point $(x,y,z)$. text/html 2018-03-30T09:54:38-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:v4chargessquareb?rev=1522428878 Is the $yz$-plane an equipotential surface? Explain. If so, what is the value of the potential? text/html 2018-03-30T09:54:38-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:v4chargessquarec?rev=1522428878 Is the $xz$-plane an equipotential surface? Explain. If so, what is the value of the potential? text/html 2016-09-23T16:33:57-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:v4chargessquared?rev=1474673637 Do you expect any other equipotential surfaces to exist? Explain. If you do expect one or more equipotential surfaces, use the Mathematica function ContourPlot3D to plot one. All plots should include a title, axis labels and a legend if appropriate. Note: providing a plot does not count as an explanation for why you would expect an equipotential surface to exist. text/html 2018-05-02T17:18:45-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:vectorpotential?rev=1525306725 Find the magnetic vector potential for a finite segment of straight wire, carrying a uniform current $I$. Put the wire on the $z$ axis, from $z_1$ to $z_2$. In addition to your usual sense-making, show the behavior of the vector potential using vector field maps. text/html 2018-05-02T17:18:45-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:vpsheet?rev=1525306725 Find the magnetic vector potential for an infinite sheet of current (you may want to perform your integral by comparing it to the electric potential due to an infinite sheet of charge). In addition to your usual sense-making, show the behavior of the vector potential using vector field maps. text/html 2019-04-05T17:13:18-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:website?rev=1554509598 Find the course website at <http://physics.oregonstate.edu/>\~{} corinne/COURSES/ph422. Read through it carefully and bring your questions to class. Don't forget to check out the Syllabus. Find the paradigms website at <http://physics.oregonstate.edu/paradigms>. Read through it carefully and bring your questions to class. text/html 2010-10-17T20:45:29-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:writingi?rev=1287373529 Using the handout ``Guiding Questions for Science Writing” to suggest topics that you should address, write up your analysis of the activity entitled Electrostatic Potential From Two Charges. You do not need to do the calculations from every case, but your analysis should include some comparison of different cases, as we discussed in class after the activity. To help us with the grading process, please turn in this writing assignment stapled separately from your other homework. text/html 2009-08-22T13:50:48-08:00 http://sites.science.oregonstate.edu/portfolioswiki/homework:ph320422questions:writingii?rev=1250974248 Using the handout ``Guiding Questions for Science Writing” as a guide, write up your solution for finding the electrostatic potential everywhere in space due to a uniform ring of charge. Be sure to include a series expansion along one of the axes of interest.