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# Differences

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activities:guides:vfvring 2014/08/07 12:03 | activities:guides:vfvring 2019/06/03 13:18 current | ||
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- | ==== 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]]. | ||

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

+ | |||

+ | * 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**. | ||

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*Preceding Activities: | *Preceding Activities: | ||

- | *[[courses:activities:vfact:vfptcharge|Electrostatic Potential due to a Point Charge]]: This small whiteboard question asks students to recall the electrostatic potential due to a point charge which results in discussions likely to include notation of the distance from the origin to a point charge. | + | *[[swbq:emsw:vfswpointpot|Electrostatic Potential due to a Point Charge]]: This small whiteboard question asks students to recall the electrostatic potential due to a point charge which results in discussions likely to include notation of the distance from the origin to a point charge. |

*[[courses:activities:vfact:vfdrawquadrupole|Drawing Equipotential Surfaces]]: This small group activity has students construct a contour plot of the electrostatic potential, level curves of equipotential, in the plane of four point charges. | *[[courses:activities:vfact:vfdrawquadrupole|Drawing Equipotential Surfaces]]: This small group activity has students construct a contour plot of the electrostatic potential, level curves of equipotential, in the plane of four point charges. | ||

*[[courses:activities:vfact:vfvisv|Visualizing Electrostatic Potentials]]: Students begin by brainstorming ways in which to represent three-dimensional scalar fields in two-dimensions and then use a Mathematica notebook to explore various representations for a distribution of point charges. | *[[courses:activities:vfact:vfvisv|Visualizing Electrostatic Potentials]]: Students begin by brainstorming ways in which to represent three-dimensional scalar fields in two-dimensions and then use a Mathematica notebook to explore various representations for a distribution of point charges. | ||