A 20 cm radius ball is uniformly charged to 70 nC. (a) What is the ball's charge density?
(b) How much charge is enclosed by spheres of radii 5, 10 and 20 cm?
(c) What is the electric field strength at points 5, 10 and 20 cm from the center?

Explanation:

A)

Density= charge/total volume eqn(1)

But volume= 4/3πr^3

r= radius= 20 cm= 0.20m

If we substitute into the volume equation, we have

volume= 4/3 * 3.142 *( 0.20)^3

= 0.0335 m^3

The volume= 0.0335 m^3

Charge=71 nC= 71×10^-9

If we substitute into eqn(1) we have

Density= (71 *10^-9C )/0.0335

= 2.11µc/m^3

B) charge enclose= Density × volume

spheres of radii are

5cm

10 cm

20 cm

Volume for 5cm

V= 4/3 * 3.142 *( 0.05)^3 = 0.0005237 m^3

charge enclose=2.11µc/m^3×0.0005237

charge enclose= 2.110 nC

Volume for 10cm

V= 4/3 * 3.142 *( 0.10)^3 = 0.004189 m^3

charge enclose= 2.11µc/m^3 ×0.004189

=8.9 nC

Volume for 20cm

V= 4/3 * 3.142 *( 0.20)^3 = 0.0335 m^3

charge enclose= 71nC