1_3 - PHY 5346 HW Set 1 Solutions Kimel 2 1.3 In general we...

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Unformatted text preview: PHY 5346 HW Set 1 Solutions Kimel 2 1.3 In general we take the charge density to be of the form f , where f is determined by r r 3 physical constraints, such as d x Q. a) variables: r, , . d 3 x dd cos r 2 dr fr R fr r R fRr R r d 3 x f R r 2 drdd r r R 4f R R 2 Q Q r 4R 2 R b fR Q 4R 2 b) variables: r, , z. d 3 x ddzrdr fr r r b fbr d 3 x f b dzdrdr r r b 2f b bL L fb 2b r b 2b c) variables: r, , z. d 3 x ddzrdr Choose the center of the disk at the origin, and the z-axis perpendicular to the plane of the disk f z R r f z R r r r where R r is a step function. 2 Q d 3 x f z R r ddzrdr 2 R f Q f R 2 2 Q r zR r R 2 d) variables: r, , . d 3 x dd cos r 2 dr f cos R r f r cos R r r r d 3 x f r cos R r dd cos r 2 dr 0 R f r r rdrd 2N rdr R 2 N Q R 0 where I've used the fact that rdrd is an element of area and that the charge density is uniformly distributed over area. Q r cos R r R 2 r ...
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This note was uploaded on 01/10/2012 for the course PHYSIS 506 taught by Professor Smith during the Spring '08 term at University of Arkansas Community College at Morrilton.

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