hw8_solutions

hw8_solutions - Solutions for Homework 8, Math 20E, Winter...

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Unformatted text preview: Solutions for Homework 8, Math 20E, Winter 2009 Page 559 Problem 5 Let P ( x, y ) = f ( x ) and Q ( x, y ) = f ( y ). Then P y = y f ( x ) = 0 and Q x = x f ( y ) = 0, since f ( x ) does not depend on y and f ( y ) does not de- pend on x . Thus by corollary 1 on page 557, there is a function g ( x, y ) such that F = g . Problem 6a Let r ( x, y, z ) = ( x, y, z ) and r ( x, y, z ) = ( x 2 + y 2 + z 2 ) 1 2 = k r ( x, y, z ) k . Then 1 r = ( x 2 + y 2 + z 2 )- 1 2 , so 1 r = (- 1 2 ( x 2 + y 2 + z 2 )- 3 2 (2 x ) ,- 1 2 ( x 2 + y 2 + z 2 )- 3 2 (2 y,- 1 2 ( x 2 + y 2 + z 2 )- 3 2 (2 z )) = (- x r 3 ,- y r 3 ,- z r 3 ) =- r k r k 3 . Problem 6b There are many ways to describe what it means to move a particle to . Here is one: Since F = 1 r , we know that the work done in moving a particle from r to another point q is independent of the path along which the particle travels (theorem 7 on page 551), and in fact for any curve ( t ) connecting them (oriented to start at r and end at q...
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This note was uploaded on 01/30/2010 for the course MATH 20E 20E taught by Professor Enright during the Fall '09 term at UCSD.

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hw8_solutions - Solutions for Homework 8, Math 20E, Winter...

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