Find the volume charge density of a non-conducting sphere of radius 10 cm and the electric field at 20 cm from the center.

Question

A non-conducting sphere of radius 10 cm carries a charge of uniformly distributed throughout its volume. At 5 cm from the centre of the sphere, the electric field is 2000 N/C and its orientation points outwards. Find a) the volume charge density of the sphere; b) the modulus of the electric field at 20 cm from the centre.

Answer 1

a) EA=Q/ε ... E=2000 n/m @ r=.05m thus Q=2000(4π.05²)ε. ρ=Q/volume=Q/(4/3π.05³) =1.2E5ε. If ε=8.85E-12 then ρ=1.06*10^-6 C/m³.

b) Assuming modulus means flux then φ = ρ(4/3π(.1)³/8.85E-12 = 37.6 N-m