Question

The figure shows a spherical shell with uniform volume charge density ρ = 2.17 nC/m³, inner radius a = 10.4 cm, and outer radius b = 3.0a. What is the magnitude of the electric field at radial distances (a) r = 0; (b) r = a/2.00, (c) r = a, (d) r = 1.50a, (e) r = b, and (f) r = 3.00b?

Answer 1

For (a), (b), (c) using Gauss’s law, we find
E = 0
For (d), (e) a ≤ r ≤ b
The enclosed charge:
(q)enc = ρ*V = ρ*(4/3πr^2 - 4/3a^3)

E = 1/4πεo * qenc/r^2

E = 1/4πεo * (q)total/r^2 = 1/4πεo * ρ*4/3π(b^3-a^3)/r^2

E = ρ/3εo * b^3-a^3/r^2

(d)

E = (2.17*10^-9C/m3/3*8.85*10^-12)*(3.0*0.104)^3-(0.104)^3/(1.50*0.104) = 1.906*10^-11NC

(E)

= (2.17*10^-9C/m3/3*8.85*10^-12)*(3.0*0.104)^3-(0.104)^3/(3.0*0.104) = 9.532*10^-12NC
(F)

= (2.17*10^-9C/m3/3*8.85*10^-12)*(3.0*0.104)^3-(0.104)^3/3*(3.0*0.104) = 3.177*10^-12NC