A nonconducting solid sphere of radius 11.6 cm has a uniform volume charge density. The magnitude of the electric field at 23.2 cm from the sphere's center is 1.89 103 N/C.

(a) What is the sphere's volume charge density? µC/m3

(b) Find the magnitude of the electric field at a distance of 5.00 cm from the sphere's center. N/C

Answer: a) 1.76 μC/m^3; b) 40.73 * 10^3 N/C

Explanation: In order to solve this problem we have to use the Gaussian law, in this sense we have:

∫E. dS = Q inside/εo then we have:

E * 4*π*r = ρ * Volume/εo

then

ρ = E4*π * εo*r^2/Volume) = E*r^2 / (k * (4/3) * π*R^3) where R is the radius of the sphere

ρ = 0.232^2*1,89*10^3 / (6.54 * 10^-3*9*10^9) = 1.76 μC/m^3

The electric field is given by:

E = k*Vol*ρ/r^2 for r = 5cm

E = 9*10^9*6.54~ 10^-3 * 1.73*10^-6 / (0.0025) = 40.73 * 10^3 N/C