hw2 - Physics 6346, Electromagnetic Theory I Fall 2000...

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Physics 6346, Electromagnetic Theory I Fall 2000 Homework 2 Due Friday, September 8, 5:00 p.m. Reading: Read Ch. 1 (again). 1. Potential for the hydrogen atom. This is essentially Jackson 1.5 done in reverse. Start with the time averaged electron charge density ρ ( r )= - q α 3 8 π e - αr , (1) and a point charge q at the origin, compute the electric field using Gauss’s law, and then find Φ( r ) by integration. You should find Jackson’s Φ( r ). What is the numerical magnitude of E at the typical atomic distance of 1 ˚ A? 2. Charged ring. A circular ring of radius R carries a uniformly distributed charge q . The ring is centered at the origin of the x - y plane, so that the z -axis is the symmetry axis. (a) Find the electrostatic potential on the z -axis of the ring. (b) Find the potential at any point in space. You can express the integral as an elliptic integral or a hypergeometric function, or as an expansion in Legendre functions (see Jackson , p. 91). (c) A positive test charge is located at the center of the ring. Is this a position of
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This note was uploaded on 11/12/2011 for the course PHY 6346 taught by Professor Staff during the Fall '08 term at University of Florida.

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hw2 - Physics 6346, Electromagnetic Theory I Fall 2000...

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