Question

In the figure the sphere of radius R is solid and non-conductive and has a uniform charge volumetric distribution p0. A spherical shell with inner radius 2R and outer radius 3R is concentric with the sphere and unloaded. Find, in terms of p0 and R: a) the value of the electric charge in the sphere, b) the magnitude of the electric field at a radial distance r - 2.5R, c) the value of the surface charge density induced in the inner surface of the spherical shell (r -2R), and d) the charge density induced on the outer surface of the spherical shell (r-3R). 3R 2R

Answer 1

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Volume of Solid sphere = 4/3 times R^3 Volumetric charge density of Solid sphere = rho_0 So charge = (4/3 pi R^3)rho^0 a) So value of electric charge = 4/3 pi R^3 rho^0 b) As we know the electric Field inside a conductor is 0, So at r = 2.5 R electric Field is zero. E = 0 c) Due to induction a opposite charge will appear on the inner surface of hallow conductor. So q = -(4/3 pi R^3)rho^0 surface charge density = q/4 pi(2R)^2 = -R rho^0/12 d) On the outer surface, surface charge density = q/4 pi(3R)^2 = (4/3 pi R^3)rho^0/4 pi (3R)^2 = R rho^0/27