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Unformatted text preview: Massachusetts Institute of Technology Department of Physics 8.022 Spring 2004 Assignment 3: Electric potential Post date: Thursday, February 19th Due date: Thursday, February 26th Be sure to write your name and section number on your pset Please staple multiple pages together NOTE: Only 75 points are assigned on this pset. If you completed pset 0, 25 points will be added to your score. 1. Vector calculus identities (10 pts): (a) Curl of gradient is zero: show that ~ ~ f = 0 for any scalar function f . (This can be done very simply using Stokes theorem.) (b) Divergence of curl is zero: show that ~ ~ ~ F = 0 for any vector function ~ F . (This can be done very simply using Gausss theorem see Purcell problem 2.16.) (c) Associativity of divergence: show that ~ f ~ F = f ~ ~ F + ~ F ~ f . (d) Associativity of curl: show that ~ f ~ F = f ~ ~ F + ~ f ~ F ....
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