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A unifrom electric field of strengthE = 100 V//mis generatedinside a ball made of uniformistropicdielectricwith permitivityepsilon = 5.00. The radiusof the ball is R = 3.0 cm. Find the maximum surfacedensityof the boundchagres and the total boundcharge of one sign. |
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Answer» Solution :Within the ball the electric field can be RESOLVED into normal and tangential components. `E_(n) = E cos theta, E_(r ) = E SIN theta` Then, `D_(n) = epsilon epsilon_(0) E cos theta` and`P_(n)= (epsilon - 1) epsilon_(0) E cos theta` or, `sigma' = (epsilon - 1) epsilon_(0) E cos theta` so, `sigma_(max) = (epsilon - 1) epsilon_(0) E`, and TOTAL of ONE sign, `q' = int_(0)^(1) (epsilon - 1) epsilon_(0) E cos theta 2 pi R^(2) d ( cos theta) = pi R^(2) epsilon_(0)(epsilon - 1) E` (Since we are intersted in the total CHARGE of one signwe mustintergative`cos theta` from0 to 1 only). 
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