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# Differences

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activities:guides:vfvring 2019/05/30 07:56 | activities:guides:vfvring 2019/06/03 13:18 current | ||
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* If you are doing this activity without having had students first create power series expansions for the electrostatic potential due to two charges, students will probably find this portion of the activity very challenging. If they have already done the <html><a href="http://www.physics.oregonstate.edu/portfolioswiki/doku.php?id=activities:main&file=vfvpoints">Electrostatic potential due to two points</a></html> activity, or similar activity, students will probably be successful with the $z$ axis case without a lot of assistance because it is very similar to the $y$ axis case for the two $+Q$ point charges. However, the $y$ axis presents a new challenges because the ``something small'' is two terms. It will probably not be obvious for students to let $\epsilon = {2R\over r}\cos\phi' + {R^2 \over r^2}$ (see Eq. 17 in the solutions) and suggestions should be given to avoid having them stuck for a long period of time. Once this has been done, students may also have trouble combining terms of the same order. For example the $\epsilon^2$ term results in a third and forth order term in the expansion and students may not realize that to get a valid third order expansion they need to calculate the $\epsilon^3$ term. | * If you are doing this activity without having had students first create power series expansions for the electrostatic potential due to two charges, students will probably find this portion of the activity very challenging. If they have already done the <html><a href="http://www.physics.oregonstate.edu/portfolioswiki/doku.php?id=activities:main&file=vfvpoints">Electrostatic potential due to two points</a></html> activity, or similar activity, students will probably be successful with the $z$ axis case without a lot of assistance because it is very similar to the $y$ axis case for the two $+Q$ point charges. However, the $y$ axis presents a new challenges because the ``something small'' is two terms. It will probably not be obvious for students to let $\epsilon = {2R\over r}\cos\phi' + {R^2 \over r^2}$ (see Eq. 17 in the solutions) and suggestions should be given to avoid having them stuck for a long period of time. Once this has been done, students may also have trouble combining terms of the same order. For example the $\epsilon^2$ term results in a third and forth order term in the expansion and students may not realize that to get a valid third order expansion they need to calculate the $\epsilon^3$ term. | ||

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==== Activity: Wrap-up ==== | ==== Activity: Wrap-up ==== | ||

- | * Discuss which variables are variable and which variables are held constant - Students frequently think of anything represented by a letter as a `variable' and do not realize that for each particular situation certain variables remain constant during integration. For example students frequently do not see that the $R$ representing the radius of the ring is held constant during the integration over all space while the r representing the distance to the origin is varying. Understanding this is something trained physicists do naturally while students frequently don't even consider it. This is an important discussion that helps students understand this particular ring problem and also lays the groundwork for better understanding of integration in a variety of contexts. For more information on this topic, see [[whitepapers:variables:start|Students understanding of variables and constants]]. | + | * Discuss which quantities are variable and which variables are held constant - Students frequently think of anything represented by a letter as a `variable' and do not realize that for each particular situation certain quantities remain constant during integration. For example students frequently do not see that the $R$ representing the radius of the ring is held constant during the integration over all space while the r representing the distance to the origin is varying. Understanding this is something trained physicists do naturally while students frequently don't even consider it. This is an important discussion that helps students understand this particular ring problem and also lays the groundwork for better understanding of integration in a variety of contexts. For more information on this topic, see [[whitepapers:variables:start|Students understanding of variables and constants]]. |

* Emphasize that while one may not be able to perform a particular integral, the power series expansion of that integrand can be integrated **term by term**. | * Emphasize that while one may not be able to perform a particular integral, the power series expansion of that integrand can be integrated **term by term**. |