Problem 1 [10 points] (a) Calculate the electric potential due to a uniformly charged annulus of inner radius R₁ and outer radius R₂ along the central axis. The surface charge density is o. (b) At distance +x from the disk, still on axis, find the electric field by taking the derivative of the electric potential. (c) Show that you get the same result by considering the potential due to a positively charged disk with charge density +o and radius R₂ with a smaller negatively charged disk with charge density - and radius R₁. This is the principle of superposition. The potential for a charged disk is derived in the textbook. R₂ X R₁ (d) Verify that you will get simple harmonic motion for small displacement near the center, just as for the charged ring. You do not need to do a full calculation- just show the relevant dependence of the field near the origin.

Problem 1 [10 points] (a) Calculate the electric potential due to a uniformly charged annulus of inner radius R₁ and outer radius R₂ along the central axis. The surface charge density is o. (b) At distance +x from the disk, still on axis, find the electric field by taking the derivative of the electric potential. (c) Show that you get the same result by considering the potential due to a positively charged disk with charge density +o and radius R₂ with a smaller negatively charged disk with charge density - and radius R₁. This is the principle of superposition. The potential for a charged disk is derived in the textbook. R₂ X R₁ (d) Verify that you will get simple harmonic motion for small displacement near the center, just as for the charged ring. You do not need to do a full calculation- just show the relevant dependence of the field near the origin.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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