http://sites.science.oregonstate.edu/portfolioswiki/ 2020-01-26T17:09:44-08:00 http://sites.science.oregonstate.edu/portfolioswiki/ http://sites.science.oregonstate.edu/portfolioswiki/lib/images/favicon.ico text/html 2014-09-09T10:31:16-08:00 http://sites.science.oregonstate.edu/portfolioswiki/whitepapers:sequences:1dintegration?rev=1410283876 Integration in One Dimension Students entering into upper-division physics courses are typically familiar and comfortable with integration as taught in mathematics courses. In physics, there is additional language and interpretation which accompany integration. By reintroducing integration early in upper-division courses, many common student difficulties which arise in electricity and magnetism and other physics courses can be addressed. text/html 2014-10-06T13:38:37-08:00 http://sites.science.oregonstate.edu/portfolioswiki/whitepapers:sequences:1dinternalenergy?rev=1412627917 Internal Energy of a One Dimensional System This sequence of activities introduces integration experimentally by quickly building to have students find the Internal Energy of the "Derivative Machine" of a nonlinear spring system. This sequence can be used with a background of introductory physics and calculus courses because it requires only a brief introduction to energy, work, and integration. This sequence can precede or follow Representations of Ordinary Derivatives which does a similar s… text/html 2014-08-13T12:18:17-08:00 http://sites.science.oregonstate.edu/portfolioswiki/whitepapers:sequences:amperelaw?rev=1407957497 Ampere's Law The integral form of Ampere's law is used to find the magnetic field in situations with high symmetry. Clean, coherent symmetry arguments are fundamental to the use of Ampere's law which can be developed by using Proof by Contradiction. There must be a sufficient amount of symmetry in the current distribution so that the field can be pulled out of the flux integral. In order to do this, the symmetry of the current distribution is used to make assumptions about the components and d… text/html 2014-08-12T13:34:50-08:00 http://sites.science.oregonstate.edu/portfolioswiki/whitepapers:sequences:boundary?rev=1407875690 Boundary Conditions Knowing how electromagnetic fields change across boundaries is a common goal in undergraduate electricity and magnetism courses. In this sequence, students explore how the components of electric and magnetic fields act at a boundary of a sheet of charge and a sheet of current. This sequence follows the derivations of boundary conditions found in the Griffiths text--sections 2.3.5 and 5.4.2 for electrostatics and magnetostatics respectively. In order to understand this appro… text/html 2016-02-09T11:57:33-08:00 http://sites.science.oregonstate.edu/portfolioswiki/whitepapers:sequences:complex?rev=1455047853 Visualizing Complex Numbers This sequence of activities introduces students to a kinesthetic way of representing complex-valued numbers and vectors. Students use their left arm as an Argand diagram to represent various complex numbers and coefficients of spin-1/2 systems. The sequence begins with individual students representing complex numbers and builds to pairs of students, representing the two-component complex-valued vectors of spin-1/2 systems. These activities provide students with a c… text/html 2008-07-11T08:01:30-08:00 http://sites.science.oregonstate.edu/portfolioswiki/whitepapers:sequences:computationalpotentialspotentials?rev=1215788490 One of our first computational exercises is the culmination of a sequence of activities that asks students to represent the electrostatic potential due to a ring of charge in several different ways. Working in small groups, students first find an expression for the potential, valid everywhere in space. Their job is to take a general, abstract equation for the potential due to a continuous distribution of charge and, wrestling through the geometry of the problem, come up with an equation that re… text/html 2019-07-22T07:12:39-08:00 http://sites.science.oregonstate.edu/portfolioswiki/whitepapers:sequences:curvcoordsseq?rev=1563804759 Curvilinear Coordinates This sequence introduces cylindrical and spherical coordinate systems. While middle-division students may have been introduced to the cylindrical and spherical coordinates themselves, in a multivariable calculus course, they have almost certainly NOT been introduced to the basis vectors such as $\hat{r}$, $\hat{\theta}$, etc. that are adapted to them. text/html 2008-08-07T14:16:16-08:00 http://sites.science.oregonstate.edu/portfolioswiki/whitepapers:sequences:diffeq?rev=1218143776 text/html 2014-08-13T12:20:53-08:00 http://sites.science.oregonstate.edu/portfolioswiki/whitepapers:sequences:differentialmaxwell?rev=1407957653 The Differential Form of Maxwell's Equations Having a thorough understanding of the differential operations provides students with a concrete means by which to interpret Maxwell's equations and transition from the integral to differential form of the equations. The sequence is split into two parts which separately address divergence and curl to build to the Gauss and Ampere Maxwell equations for both electric and magnetic fields. This sequence is assuming static fields and therefore does not b… text/html 2014-10-08T17:21:53-08:00 http://sites.science.oregonstate.edu/portfolioswiki/whitepapers:sequences:directint?rev=1412814113 Direct Integration to Determine Electrostatic Potential Activities The Distance Between Two Points--Star Trek(Estimated time: 20-30 minutes)Total Charge(Estimated time: 30 minutes)Electrostatic Potential due to a Ring(Estimated time: 40 minutes, Wrap Up: 10 minutes)``” text/html 2016-06-28T13:24:51-08:00 http://sites.science.oregonstate.edu/portfolioswiki/whitepapers:sequences:eename?rev=1467145491 Name The Experiment Activities This sequence of activities is designed to provide an opportunity for students to connect partial derivatives with physical experiments in thermodynamics. Small groups are tasked with designing experiments which could be used to measure a partial derivative from thermodynamics. These activities are intended to encourage students to actively think about the physical meaning of partial derivatives throughout thermodynamics problems and demonstrate that some are dif… text/html 2018-08-17T12:50:42-08:00 http://sites.science.oregonstate.edu/portfolioswiki/whitepapers:sequences:eepdm?rev=1534535442 The Partial Derivative Machine When students are first introduced to the common manipulations of thermodynamics they often have issues connecting the presented mathematics with the physical measurements the math represents. The Partial Derivatives Machine (PDM) allows students to investigate these relationships while gaining a deep understanding of the limitations placed on measurements in thermodynamics. The following sequences use the PDM to explore various derivatives and integrals through … text/html 2014-08-25T09:45:09-08:00 http://sites.science.oregonstate.edu/portfolioswiki/whitepapers:sequences:eigenfunctions?rev=1408985109 Introducing Eigenfunctions In order to appreciate the parallels between finite quantum systems, such as spin-1/2 systems, and infinite quantum systems, such as the infinite potential well, students need to extend their understanding of vector spaces to include sets of functions. This requires transitioning from a system with a discrete set of eigenstates to a continuous system where the eigenstates are eigenfunctions. Important new ideas related to the concept of eigenfunctions are differentia… text/html 2015-08-15T10:10:37-08:00 http://sites.science.oregonstate.edu/portfolioswiki/whitepapers:sequences:flux?rev=1439658637 The Geometry of Flux These activities are intended to address the geometric nature of flux; flux, as used in physics, is the sum of the normal components of a vector field on a surface. Gauss's law uses a flux integral to find the electric field in situations with high symmetry. The first three activities are used in rapid succession to emphasize this geometry without introducing Gauss's law explicitly and make a stand-alone introduction to the geometry of flux. The sequence culminates in usin… text/html 2014-09-30T16:45:04-08:00 http://sites.science.oregonstate.edu/portfolioswiki/whitepapers:sequences:fluxintegrals?rev=1412120704 Flux Integrals Flux integrals are used in electricity and magnetism to find total current and in Gauss's law. Therefore, it is important for physics students to be mathematically and conceptually proficient with flux. Mathematically, flux has the differential area vector, $d\vec{A}$, which is likely new to students in cylindrical and spherical coordinates. Conceptually, the flux of a static vector field is the amount of vector fields that “points through” a given area in the plane of the a… text/html 2014-06-18T15:10:44-08:00 http://sites.science.oregonstate.edu/portfolioswiki/whitepapers:sequences:gauss?rev=1403129444 Gauss' Law and Ampere's Law Activities Total ChargeVisualizing Electric FluxGauss's LawAmpere's Law text/html 2014-08-06T11:24:16-08:00 http://sites.science.oregonstate.edu/portfolioswiki/whitepapers:sequences:gausslaw?rev=1407349456 Gauss's Law Gauss's law equates the total charge to the flux of the electric field by $\int{ \vec{E} \cdot d\vec{A}}=\frac{Q_{enclosed}}{\epsilon_0}$. This sequences develops the essential components of using Gauss's law: making symmetry arguments, calculating total charge, and using a flux integral to find the electric field. text/html 2014-08-06T11:06:44-08:00 http://sites.science.oregonstate.edu/portfolioswiki/whitepapers:sequences:gradientseq?rev=1407348404 Geometry of the Gradient The gradient is used to relate the electric field, a vector field, to the electrostatic potential, a scalar field, by $ \vec{E} = - \vec{\nabla} V $. Many students entering into middle-division electricity and magnetism courses may have been introduced to the gradient in vector calculus and may be comfortable with calculating the gradient. However, many students may not understand the geometric meaning of the gradient which can be used to physically understand the rel… text/html 2014-09-08T12:01:43-08:00 http://sites.science.oregonstate.edu/portfolioswiki/whitepapers:sequences:integratecharge?rev=1410202903 Integration in Curvilinear Coordinates to Determine Total Charge Integration using curvilinear coordinates has been introduced to most students in a multivariable calculus course prior to entering into upper-division electricity and magnetism courses, however, some students may not carry those skills immediately into physics. By reintroducing curvilinear coordinates, with the physics convention for $\theta$ and $\phi$, in a physical context, students can determine the total charge of a line, s… text/html 2014-09-11T15:28:33-08:00 http://sites.science.oregonstate.edu/portfolioswiki/whitepapers:sequences:integratecharge2?rev=1410474513 Total Charge in Curvilinear Coordinates Activities Acting Out Charge Density(Estimated time: 10 minutes)“”Total Charge in Rectangular Coordinates(Estimated time: )Curvilinear Coordinates(Estimated time: )Scalar Distance, Area, and Volume Elements(Estimated time: )Pineapples and PumpkinsPineapples and Pumpkins(Estimated time: )Scalar Distance, Area, and Volume ElementsTotal Charge(Estimated time: 30 minutes) text/html 2014-09-02T15:09:26-08:00 http://sites.science.oregonstate.edu/portfolioswiki/whitepapers:sequences:planewaves?rev=1409695766 Plane Waves By the time students are in their senior year, most have had some experience with planes, but many students are unable to say what's planar about plane waves. This sequence of activities helps students understand $\vec{k}\cdot\vec{r}$ and visualize different representations of plane waves commonly used in physics. Some of the activities in this sequence were the first to be designed and have even found their way in TA training sessions and teaching seminars. We often use these acti… text/html 2014-06-18T15:07:03-08:00 http://sites.science.oregonstate.edu/portfolioswiki/whitepapers:sequences:potentials?rev=1403129223 Representations of Fields One of the difficulties many students have is connecting an algebraic expression with the associated geometry. This is particularly noticeable when students study potential and force fields. This sequence of activities aims to help students understand the geometry of scalar and vector fields, and how to connect them to algebraic expressions. text/html 2016-02-15T14:06:45-08:00 http://sites.science.oregonstate.edu/portfolioswiki/whitepapers:sequences:qmoperatorseq?rev=1455574005 Quantum Operators Spin 1/2 systems are the simplest quantum systems and the Stern-Gerlach experiment is at the heart of quantum measurement theory. From our research [Making sense of quantum operators, eigenstates, and quantum measurements], we found that many of our students share the common misunderstanding that the eigenvalue equations $$S_z \vert \pm \rangle = \pm\frac{\hbar}{2} \vert \pm \rangle$$ is a mathematical description of what happens inside the Stern Gerlach device. Then they a… text/html 2014-08-04T13:18:39-08:00 http://sites.science.oregonstate.edu/portfolioswiki/whitepapers:sequences:qmring?rev=1407183519 Quantum Calculations for a Particle Confined to a Ring This sequence of activities gives students a chance to practice a variety of calculations for a specific system: a quantum particle confined to a ring. In particular, these activities help students to see that all of the calculations that they have done previously in the Spins and Waves courses can be applied to these new systems. In addition to the main goal(s) for each activity, they all provide an opportunity for students to deal with d… text/html 2011-07-06T11:17:21-08:00 http://sites.science.oregonstate.edu/portfolioswiki/whitepapers:sequences:qmsystems?rev=1309976241 SpinsSpinsWavesWavesCentral ForcesCentral ForcesCentral ForcesQuantum CapstoneQuantum Capstone text/html 2012-03-23T17:54:19-08:00 http://sites.science.oregonstate.edu/portfolioswiki/whitepapers:sequences:qmtimeevol?rev=1332550459 SpinsSpinsSpinsSpinsTime Evolution of Infinite Well SolutionsSGAWavesTime Evolution of a Gaussian Wave PacketWavesTime Development of a Particle Confined to a RingSGACentral Forces text/html 2014-09-30T16:43:49-08:00 http://sites.science.oregonstate.edu/portfolioswiki/whitepapers:sequences:repderivatives?rev=1412120629 Representations of Ordinary Derivatives Students entering into middle-division physics courses often have a limited working definition of the derivative and tend to consider the derivative an analytic procedure. This sequence introduces the derivative using many different representations and requires that students move between representations of the derivative. Additionally, differences in typical ways which mathematicians and physicists may different in their respective disciplines regarding … text/html 2014-10-03T15:41:27-08:00 http://sites.science.oregonstate.edu/portfolioswiki/whitepapers:sequences:repscalarfield?rev=1412376087 Representations of Two-Dimensional Scalar Fields This sequence can be used following Representations of Ordinary Derivatives sequence at the beginning of middle-division courses to quickly introduce students to using multiple representations. These two sequences do not require knowledge beyond what is introduced in introductory physics and calculus courses, however, they can be used to discuss previous information in more detail. text/html 2019-07-22T06:58:36-08:00 http://sites.science.oregonstate.edu/portfolioswiki/whitepapers:sequences:scalarfieldseq?rev=1563803916 The Geometry of Scalar Fields This sequence introduces various representations of scalar fields in the context of electrostatic potentials. While middle-division students have lots of experience with representations of functions of a single independent variable, many still need help with visualizing functions of two (or especially three) independent variables. This sequence introduces: equipotential curves and surfaces (contour plots), tangible dry-erasable plastic surfaces, computer-generate… text/html 2015-07-28T15:53:46-08:00 http://sites.science.oregonstate.edu/portfolioswiki/whitepapers:sequences:spspins?rev=1438124026 Stern-Gerlach Simulations These labs all use a java program called SPINS that simulates Stern-Gerlach experiments with spin-$\frac{1}{2}$ and spin-$1$ particles. The software runs on all platforms and can be downloaded from the SPINS home page. text/html 2019-07-22T11:43:02-08:00 http://sites.science.oregonstate.edu/portfolioswiki/whitepapers:sequences:start?rev=1563820982 Sequences are ~3 or more activities that are used together to explore a particular topic from several different viewpoints to allow students to explore how information and ideas tie together. E & M Sequences Curvilinear CoordinatesGeometry of Scalar FieldsRepresentations of Two-Dimensional Scalar FieldsGeometry of Vector Fields:Superposition of Electrostatic Potentials due to Point Charges text/html 2014-10-02T12:20:46-08:00 http://sites.science.oregonstate.edu/portfolioswiki/whitepapers:sequences:superpositionpot?rev=1412277646 Superposition of Electrostatic Potential due to Point Charges This sequence of activities can directly follow the Representations of Two-Dimensional Scalar Fields sequence. Activities Recall the Electrostatic Potential due to a Point Charge(Estimated time: 5 minutes)Lecture on Electrostatic Potential and Superposition of Charges(Estimated time: 20 minutes)Recall the Electrostatic Potential due to a Point ChargeDrawing Equipotential Surfaces(Estimated time: 45 minutes)PhET: Charges and Fields … text/html 2014-08-13T11:59:45-08:00 http://sites.science.oregonstate.edu/portfolioswiki/whitepapers:sequences:vectorfieldseq?rev=1407956385 Geometry of Vector Fields After students have spent time working with both the algebra and geometry of scalar fields, they move on to vector fields in the context of electric fields. Vector fields can be considered more complicated than scalar fields because at each point there is a vector with both a magnitude and direction while scalar fields have one value at each point. Not only does this increase the difficulty in representing the field, but there are also additional properties of vector … text/html 2012-07-08T14:37:07-08:00 http://sites.science.oregonstate.edu/portfolioswiki/whitepapers:sequences:vectorspaces?rev=1341783427 OscillationsSpinsWavesCentral ForcesCentral ForcesCentral ForcesE&M CapstoneQuantum Capstone text/html 2014-06-19T12:04:52-08:00 http://sites.science.oregonstate.edu/portfolioswiki/whitepapers:sequences:veff?rev=1403204692 Reconciliation of Effective Potentials with Orbit Shape A valuable sequence of activities arises during our discussion of classical orbits that illustrates how computational work must be integrated with other activities to achieve the pedagogical goal. We would like our students to understand how the shape of the orbit depends on various physical parameters such as reduced mass or the z-component of angular momentum and how this shape can be predicted by an effective potential diagram. text/html 2009-03-24T22:01:28-08:00 http://sites.science.oregonstate.edu/portfolioswiki/whitepapers:sequences:veigenfuctions?rev=1237957288 A central feature of all of these activities is the use of color to plot the probability density as a function on which the particle actually lives. Many students, at this stage in their development, are still not asking what the “vertical” axis means. When we use conventional graphs, that depict wavey graphs, students tend to interpret them as the particle waving back and forth physically in space. (Insert reference.) Trust us. This is what you really need to try. text/html 2014-07-25T14:17:22-08:00 http://sites.science.oregonstate.edu/portfolioswiki/whitepapers:sequences:veigenfunctions?rev=1406323042 Visualizing Eigenfunctions We have a number of Mathematica/Maple-based activities that allow students to visualize quantum mechanical eigenfunctions. For particle in a box or the particle confined to a ring, since the functions are quite simple, the visualizations explore the time dependence of the wave functions and their probabilities. For more complicated wave functions, such as the rigid rotor or the hydrogen atom, we currently have activities which explore the probability density only. … text/html 2014-08-15T11:08:41-08:00 http://sites.science.oregonstate.edu/portfolioswiki/whitepapers:sequences:wavepropcoax?rev=1408126121 Wave Propagation in Coaxial Cable Activities Creating a Pressure-like Wave in a Coaxial Cable(Estimated time: 15 minutes)Pressure Wave Simulation(Estimated time: 5 minutes)Wave Propagation in a Coaxial Cable(Estimated time: 90-120 minutes) text/html 2014-06-19T12:01:05-08:00 http://sites.science.oregonstate.edu/portfolioswiki/whitepapers:sequences:wavevel?rev=1403204465 Wave Velocities: Material Velocity & Phase Velocity Middle division students need to understand the three different velocities that are relevant for describing wave propagation. We use a sequence of activities to introduce and build conceptual and mathematical understanding of these different velocities.