Question

The electric field everywhere on the surface of a thin, spherical shell of radius 0.770 m is of magnitude 892 N/C and points radially toward the center of the sphere. (a) What is the net charge within the sphere's surface

Answer 1

Q = 58.8 nC

Step-by-step explanation:

For distance just above the surface of the spherical shell and higher, electric field of the shell can be considered as the electric field generated by a charge Q at the center of the spherical shell:

To calculate the net charge within the sphere's surface you use the following formula:

`E=k(Q)/(R^2)` (1)

Q: net charge of the spherical shell

R: radius of the sphere = 0.770m

E: magnitude of the electric field for points just above the sphere's surface = 892N/C

k: Coulomb's constant = 8.98*10^9 Nm^2/C^2

You solve the equation (1) for Q and replace the values of the other parameters:

`Q=(R^2E)/(k)=((0.770m)^2(892N/C))/(8.98*10^9Nm^2/C^2)\\\\Q=5.88*10^(-8)C=58.8nC`

The net charge within the sphere's surface is 58.8nC