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EAD 234A: E&M Homework #1 Due Thursday, January 14, 2005 1. Use Gauss' law to find the electric field when the charge density is: (a) () { } 2 0 exp x x ρρ κ =− Express the answer in Cartesian coordinates. (b) { } 22 0 ,e x p x yx y + Express the answer in cylindrical coordinates (c) { } 222 0 ,, e x p xyz x y z + + Express the answer in spherical 2. ( a) Find the force per unit length between the halves of a uniformly charged sheet with infinite length and width W by superposing the forces between infinite charged lines. Note that each half has a width W/2 and infinite length. (b) Find the force per unit area between the halves of a uniformly charged brick with infinite length and width and thickness T by superposing the forces between infinite charged sheets. Note that each half has a thickness T=2 and infinite area. 3. We wish to employ superposition in solving some simple electrostatics problems. (a) Find E ( r ) inside and outside a uniformly charged spherical shell by superposing the electric fields produced by a collection of charged rings.

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