A copper sphere 0250m in radius has a charge of 400x107 C Co

A copper sphere 0.250m in radius has a charge of +4.00x10^-7 C. Copper is a conductor; the charge is uniformly distributed on the surface of the sphere. What is the magnitude of the electric field at the following distances from the center of the sphere:

a).200m

b).300m

c).500m

Gauss\' Law

Solution

a)
use Gaussian surface for r = 0.200 m, charge enclosed = 0
Use:
E*A = Qenclosed / epsoleleno
Since Qenclosed = 0, E will be 0
Answer: 0 N/C

b)
use Gaussian surface for r = 0.300 m, charge enclosed = 4.00*10^-7 C
Use:
E*A = Qenclosed / epsoleleno
E*(4*pi*r^2) = (4.00*10^-7) / (8.854*10^-12)
E*(4*pi*0.300^2) = 4.518*10^4
E = 3.994*10^4 N/C
Answer: 3.994*10^4 N/C

c)
use Gaussian surface for r = 0.300 m, charge enclosed = 4.00*10^-7 C
Use:
E*A = Qenclosed / epsoleleno
E*(4*pi*r^2) = (4.00*10^-7) / (8.854*10^-12)
E*(4*pi*0.500^2) = 4.518*10^4
E = 1.438*10^4 N/C
Answer: 1.438*10^4 N/C