Conceptual Understanding in Introductory Physics XXIV: Distance Variations of Fields and Forces

This question was inspired by chapters 13, 14, and 15 of Matter & Interactions and would, I think, make a good final exam question even in courses where M&I isn’t used. The story line in those chapters makes a wonderful progression through different charge distributions and their fields and interactions with other similar charge distributions. The rather obvious patterns in this progression are worth emphasizing. They seem to be a consequence of superposition, which is one of most conceptually astounding ideas in physics.

Make a table giving at least one charge distribution, or combination of distributions, that gives rise to an electric field or electric interaction (force) that varies as 1/(r^n) where n = 0, 1, 2, …, 9. It may be the case that not all values of n are represented in the table. 

I can think of at least one example where a double digit value of n is needed, but most courses don’t deal with that situation.


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