ImageCharge4GrondedSphericalComductor

ImageCharge4GrondedSphericalComductor - aR cos + q 4 1 b 2...

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Location and value of an image charge for grounded conducting sphere Consider a grounded sphere of radius R with a charge q at (0 , 0 ,a ), where a > R . We want to determine potential at every point outside the sphere. We want to simulate this situation by putting in a charge q 0 at a point (0 , 0 ,b ), where b < R . We will choose q 0 and b in such a way that the potential at any point on the sphere, i.e., V ( R,θ,φ ) = 0. The potential V ( R,θ,φ ) due to q and q 0 is given by: V ( R,θ,φ ) = q 4 π² 0 1 a 2 + R 2 - 2
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Unformatted text preview: aR cos + q 4 1 b 2 + R 2-2 bR cos = 0 q a 1 q 1 + R 2 a 2-2 R a cos + q R 1 q 1 + b 2 R 2-2 b R cos = 0 X l =0 q R l a l +1 + q b l R l +1 ! P l (cos ) = 0 q R l a l +1 + q b l R l +1 ! = 0 for every l For l = 0, this implies q =-R a q. Plugging this value of q into q R l a l +1 + q b l R l +1 = 0 gives R l a l-b l R l = 0...
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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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