ImageCharges - θ,φ ). In particular, for θ = 0 and θ =...

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Image Charge for a grounded sphere (radius R ) with a point charge q sitting at (0 , 0 ,d < R ). Consider a point charge q sitting at (0 , 0 ,d ) inside a sphere of radius R ( d < R ). Assume the image charge - q 0 situated at (0 , 0 ,d 0 ) outside the sphere. The potential φ ( ~ r ) at a point ~ r ( R,θ,φ ) (spherical coordinates) is then given by φ ( R,θ,φ ) = 1 4 π² 0 q R 2 + d 2 - 2 Rd cos θ - q 0 R 2 + d 0 2 - 2 Rd 0 cos θ (1) We want this expression to be zero for every value of (
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Unformatted text preview: θ,φ ). In particular, for θ = 0 and θ = π , we get following two equations: q R-d = q d-R and q R + d = q d + R Thus, we have R + d R-d = d + R d-R-→ d R-d = R d-R This leads to d = R 2 d and q = R d q . 1...
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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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