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A point charge qis located at the centre of a ball made of uniform istopic dielectric with permittivity epsilon.Find the polarizaion P as a function of the radiusvector rrelativeto the centreof the system, as well as the chagre q' insidea sphere whose radius is less than radius of the ball. |
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Answer» Solution :Inside the ball `vec(D) (vec( R)) = (q)/(4pi) (vec( r))/(r^(3)) = epsilon_(0) vec(E)`. ALSO`epsilon_(0) vec(E) + vec(P) = vec(D)` or `vec(P) = (epsilon - 1)/(epsilon) vec(D) = (epsilon - 1)/(epsilon) (q)/(4pi) (vec(r ))/(r^(3))` Also, `q' = -oint vec(p) .d vec(S) = - (epsilon - 1)/(epsilon) (q)/(4pi) INT d Omega = (epsilon - 1)/ (epsilon) q'` |
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