Question

The electric field everywhere on the surface of a thin, spherical shell of radius 0.750 m is of magnitude 890 N/C and points radially toward the center of the sphere. What is the net charge in nano coulomb within the sphere’s surface?

Answer 1

Answer:

55.6 nC

Explanation:

The electric field at the surface of a charged sphere has the same expression of the electric field produced by a single point charge located at the centre of the sphere and having the same charge of the sphere, so it is given by

$E=k\frac{Q}{r^2}$

where

$k=9\cdot 10^9 N m^2 C^{-2}$ is the Coulomb's constant

Q is the charge on the sphere

r is the radius of the sphere

In this problem we know

E = 890 N/C is the magnitude of the electric field on the sphere

r = 0.750 m is the radius of the sphere

So by re-arranging the equation we can find the net charge on the sphere:

$Q=\frac{Er^2}{k}=\frac{(890)(0.750)^2}{9\cdot 10^9}=5.56\cdot 10^{-8} C=55.6 nC$