A hollow, metallic, spherical shell has exterior radius 0.750 m, carries no net charge, and is supported on an insulating stand. The electric field everywhere just outside its surface is 890 N/C radially toward the center of the sphere. Explain what you can conclude about (a) the amount of charge on the exterior surface of the sphere and the distribution of this charge, (b) the amount of charge on the interior surface of the sphere and its distribution, and (c) the amount of charge inside the shell and its distribution.

a

a.) The total charge can be treated as a point charge as if the sphere were compacted to a point (by Gauss's law).The magnitude of the charge can be found by the electric field equation

            Electric Field due to a point charge at a distance is

         Here, q is charge so

So the charge on the surface would be

b

The charge on the interior surface is equal to -Q(i.e ), since the net charge is zero.It is also distributed uniformly.

c

The charge on the inside is equal to Q, inducing the charge on the inside of the shell, which in turn induces the charge on the outside. We can't say exactly how it is distributed due to Gauss's law, but we at least know it is symmetric since the field is uniform.

Explanation:

In order to get a better understanding of the solution above let get to know more about the  Gauss's law

  Gauss's law

  This law talks about the distribution of the electric that produces the electric field

 This law states that the the net flux of an electric field through a closed surface is proportional to the enclosed enveloped electric charge and we can say that an electric flux  is the product of  a given area and the electric field passing through this area.