E5chalsoln - Phy sics 7B WS E5 Challenge Solution (rev....

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Physics 7B WS E5 Challenge Solution (rev. 1.0) Page 1 E-5 Challenge Problem - Solution Classical Radius of the Electron. In this challenge problem, we will calculate a quantity known as the classical radius of the electron . a) Consider a sphere of charge, with radius R and total charge q. What is the charge density, ρ ? The volume of a sphere is V = (4/3) π R 3 . Since we are assuming that the charge q is distributed uniformly over this volume, the charge density is just ρ = q/V, so . " = q 4 3 # R 3 . b) What charge is enclosed in a sphere of radius r<R? Call this q(r). The volume enclosed by this sphere is V(r) = (4/3) π r 3 . Since we are assuming that the charge q is distributed uniformly over this volume, the charge is just q = ρ V(r), so . q ( r ) = q r 3 R 3 . c) What charge, dq, is contained in a spherical shell of width dr and radius r? There are two ways to approach this. The first is to find the volume of a spherical shell with radius r and width dr. Since dr is infinitessimal, this is just the surface area of the sphere times the width dr: dV = A(r) dr. This is the same result we would get if we found the volume by calculating V(r+dr) – V(r) to first order in dr. The surface area of a
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This note was uploaded on 11/19/2010 for the course LECTURE 1 taught by Professor Yildiz during the Fall '10 term at University of California, Berkeley.

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E5chalsoln - Phy sics 7B WS E5 Challenge Solution (rev....

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