Qestion is electrostatics?

Question

I have an electric sphere and a certain point out of the sphare.
2 cases:
1.Electric charge is distributed evenly in the volume of the sphere.
2.The same electric charge is evenly distributed in the layer of the sphere.
My question is if the Electric field outside both of these sphares ( which are of the same size) is the same or not. If it is the same then the potential of the point outside these spheres should be the same too.

Answer 1

Electric charges inside the sphere "emerge" to the surface of the sphere only if they can move. This happens whenever the sphere is solid but made from conductor stuff, i.e. metal. Otherwise, charges stay where they are.

On the other hand, Gauss Law gives the total charge enclosed within a closed surface, by integrating the lines of force over that surface. In this case, it would be pointless to calculate the charge enclosed, since we know from the outset they're equal. This does not automatically guarantee that both fields are equal, however. It only states that the surface integral of the field is the same in both cases. The fields themselves may differ greatly.

Circumstances allowing, Gauss Law may be used "in reverse" to figure out the field, given the charge enclosed is known. Mainly, this happens when we know in advance the field has an even distribution over space, from symmetry considerations.

Since you state the distribution is even in both cases, it can be expected that the field OUTSIDE the spheres be very similar. So, yes, the potential of a point outside the spheres should be essentially the same.

Answer 2

You'll need to do some calculus to get an exact answer, but Gauss's Law would seem to say the fields would be identical. It seems counterintuitive, since near the surface, you are much closer to the charges when they are at the surface than when they are uniformly distribed over the volume. I'm still trying to think of a reason Gauss's Law doesn't apply. Perhaps it's because the surface charge doesn't satisfy spherical symmetry. We also assume the conductivity of your spheres is zero, and the dielectric constant is the same as that of free space.

Answer 3

It would happen to work out by Gauss's Law that the electric field outside the sphere will be the same for both situations.

Answer 4

Static electricity is distributed evenly on the OUTER layer of the sphere (the "skin" of the sphere), whether the sphere is plain (a ball of steel) or hollow (a balloon)!