# A ball of radius R carries a positive charge whose volume density depends only on a separation r from the ball's centre

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A ball of radius R carries a positive charge whose volume density depends only on a separation r from the ball's centre as ρ = ρ0 (1 — r/R), where ρ0 is a constant. Assuming the permittivities of the ball and the environment to be equal to unity, find:

(a) the magnitude of the electric field strength as a function of the distance r both inside and outside the ball;

(b) the maximum intensity Emax and the corresponding distance rm .

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(a) Let us consider a sphere of radius r < R then charge, inclosed by the considered sphere,

Now, applying Gauss’ theorem,

(b) As‘magnitude of electric field decreases with increasing r for r > R, field will be maximum for r < R. Now, for Er to be maximum,