Question

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 1

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