Question

A solid, nonconducting sphere of radius R = 6.0cm is charged uniformly with an electrical charge of q = 12µC. it is enclosed by a thin conducting concentric spherical shell of inner radius R, the net charge on the shell is zero.

a) find the magnitude of the electrical field E₁  inside the sphere (r < R) at the distance r₁ = 3.0 cm from the center.

b) find the magnitude of the electric field E₂ outside the shell at the distance r₂ = 8.0 cm from the Sphere

c) what is the surface charge density: cd. (charge per unit) induced on the inner surface of the conducting Shell?

d) what is the electric field E_o at the center of the sphere (r₀ = 0)

Answer 1

from Gauss law,

net flux through closed surface = Qin / e0

for symmetric spherical charge distribution,

E ( 4 pi r^2) = Qin / e0

(A) Qin = q (r/R)^3

E (4 pi r^2) = q r^3 / R^3

E = (12 x 10^-6 x 0.03) / (4 pi 8.854 x 10^-12 x 0.06^3)

E = 15 x 10^6 N/C

(B) E ( 4 x pi x 0.08^2) = (12 x 10^-6)/(8.854 x 10^-12)

E = 16.85 x 10^6 N/C

(C) on inner surface, Q = - q = -12 x 10^-6 C

surface charge density = - q / (4 pi R^2)

= - 149.2 x 10^-6 C/m^2

(D) QIn = 0 so E = 0