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A smallconducting ball carryinga charge q is located in a uniforman infiniteboundary planebetweenthe dielectrics and vacumm. Find the surfacedensity of the boundchagres on the boundary plane as a function ofdistance r from the ball. Analysse the obtained result for l rarr 0. |
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Answer» Solution :`vec(E_(p)) = (q vec(r_(2)))/(4 pi epsilon_(0) r_(2)^(3)) + (q' vec(r_(1)))/(4pi epsilon_(0) r_(1)^(3)) , P` in 2 `vec(E_(p)) = (q" vec(r_(2)))/(4 pi epsilon_(0) r_(2)^(3)) , P` in 1 Using the boundary conditions, `E_(1n) = epsilon E_(2n), E_(1T) - E_(2T)` This implies `q - epsilon q' =q''` and `q + epsilon q' = epsilon q''` So,`q'' = (2q)/(epsilon + 1), q' = (epsilon - 1)/(epsilon +1) (q)/(epsilon)` Then, as earlier, `sigma' = (ql)/(2pi r^(3)) ((epsilon - 1)/(epsilon + 1)) . (1)/(epsilon)` 
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