Question

The electric field at a distance of 0.144 m from the surface of a solid insulating sphere with radius 0.384 m is 1710 n/c. assuming the sphere's charge is uniformly distributed, what is the charge density inside it? calculate the electric field inside the sphere at a distance of 0.223 m from the center

Answer 1

By Gauss' Law the sphere will appear externally as if all of the charge were concentrated at the center of the sphere.

E = K Q / r^2 = K Q / .528^2

Q = 1710 * .528^2 / 9.00E9 Coulombs

Q = 5.30E-8 Coulombs on sphere

V = 4/3 π R^3 = 4/3 π * .384^3 = .237 m^3

ρ = Q / V = 5.30E-8 / .237 = 2.23E-7 C/m^3

At .223 from center Q = 4/3 π .223^3 * ρ (charge outside this radius will not affect electric field outside .223 m)

Q = 2.23E-7 * 4/3 * π * .223^3 = 1.04E-8 Coulombs

E = 9.00E9 * 1.04E-8 / .223^2 = 1880 N/C