E_M_Chap2 - on it. You will need the Heavyside -function,...

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Chapter 2 How would you write down the volume charge densities of following objects: A ring of radius R carries a total charge Q (uniformly distributed) placed on the xy -plane with its center at the origin. ans. ρ ( ~ r ) = Q 2 πR 2 δ ( r - R ) δ ( θ - π 2 ) . A ring of radius R carries a total charge Q (uniformly distributed) placed on the z = R 2 -plane and has its center on the z -axis. ans. ρ ( ~ r ) = Q 2 πR 2 δ ( r - R ) δ ( θ - θ 0 ) . A disk of radius R has a uniform charge density
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Unformatted text preview: on it. You will need the Heavyside -function, dened below, for this problem. ( x ) = x < 1 x > 1 2 x = 0 It can be represented by 1 2 1 + x | x | . Another nice representation is ( x ) = lim 1 2 1 + tanh x . Note that lim 1 2 sec h 2 x = d ( x ) dx = ( x )....
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This note was uploaded on 01/28/2010 for the course PHYS 351 taught by Professor Gangopashyaya during the Spring '09 term at Loyola Chicago.

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