# Distribution of charge on a hollow metal sphere

A hollow metal sphere is electrically neutral (no excess charge). A small amount of negative charge is suddenly placed at one point P on this metal sphere. If we check on this excess negative charge a few seconds later we will find one of the following possibilities:

(a) All of the excess charge remains right around P.

(b) The excess charge has distributed itself evenly over the outside surface of the sphere.

(c) The excess charge is evenly distributed over the inside and outside surface.

(d) Most of the charge is still at point P, but some will have spread over the sphere.

(e) There will be no excess charge left.

Which one is correct and why?

I guess it is some kind of electrostatic induction - phenomena going on. Am I right? I understand that excess charge is distributed over hollow sphere and that negative and positive charges are distributed opposite sides, but don't know which one positive or negative go to inside surface.

• So right answer was a)? What is capacitors? – alvoutila Oct 17 '12 at 12:22

Your homework question is from http://panda.unm.edu/Courses/Malloy/PHYS161//Physics_161_Home_files/Lecture22.pdf

Which one is correct

b)

and why?

• Metal conducts.
• Charges can travel freely in a conductor.
• Like charges repel
• The charge carriers move as far apart as they can be
• The furthest apart they can be is evenly distributed over the outer surface.

I guess it is some kind of electrostatic induction - phenomena going on. Am I right?

I think not. See Wikipedia -"Electrostatic induction is a redistribution of electrical charge in an object, caused by the influence of nearby charges"

I understand that excess charge is distributed over hollow sphere

The whole charge, not just some excess (over what?), is distributed over the sphere.

negative and positive charges are distributed opposite sides

No, if there were both positive and negative charges on opposite sides they would not stay there, they would be attracted to one another and quickly cancel out.

but don't know which one positive or negative go to inside surface.

Neither.

What is capacitors?

See Wikipedia re capacitors.

• Do you mean that I would not just paste and copy? Let me tell you that this is one question from my electromagnetic conceptual test in finnish in a course. So because I went on trying to search some hint how to handle this problem for 1-3 hours, then I decided to ask this "question". – alvoutila Oct 17 '12 at 13:38
• I meant that negative and positive charges are distributed together. They are clumped together and that way they negate each other and excess charges are then distibuted evenly to over hollow sphere. What is electrostatic(not electromagnetic) induction ~ influence? I think it is charges are distributed according to the outside electric field or nearby charges. Is it true that with electroscope you can detect net charge of charged object? – alvoutila Oct 17 '12 at 15:33
• @alvoutila: I've updated my answer. "Negative and positive charges distributed together" are neutral, they cancel out. "They are clumped together" only in atoms that are therefore overall neutral. See W re electrostatic induction. Charge carriers affect the electrostatic field. No, only local charge in vicinity of electroscope. Ask followup questions separately or move to chat. – RedGrittyBrick Oct 17 '12 at 15:56
• Why chat? It looked messy there. I have only clarifying questions. What is "W re electrostatic induction"? Is it Wikipedia: electrostatic induction? I meant by "they are clumped together " that they(charges of object) are attracted to another and then they cancel out. – alvoutila Oct 17 '12 at 20:33

Yeah. The right answer would be (B) the negative charge that started on point P will be distributed evenly throughout the surface of the sphere since (as most of the commentators here have mentioned) that point P has too much negative charges in it, so the negatively charged atoms will repel each other more vigorously until they move to a place (i.e. a place NOT on point P ) where there's less negatively charged atoms. But, also note that point P will still be negatively charged just like the rest of the sphere, but now all of the sphere's surface will have the same amount of charges.

B, Since the sphere has no charge the negative charge would distribute evenly across the surface as like charges repel the push themselves away from each other.

B is correct, but this is due to the Coulomb's law, the fact that the force between charges decays as the inverse square of the distance. It is not due to the mere fact that like charges repel, as this doesn't explain why all the charges would end up at the surface. Coulomb's law can be shown to be equivalent to Gauss' law which says that the total charge contained inside a closed surface divided by $\varepsilon_0$ is equal to the integral of the component of the electric field along the outward normal of the surface over the closed surface.

A charge inside the metal will experience a total force proportional to the electric field due to all the other charges. The charge distribution can thus only be in equilibrium if the total electric field inside the metal is zero. Gauss' law then implies that any surface contained within the metal contains a charge of zero, therefore there cannot be a net charge anywhere inside the metal when the charge distribution has settled down.

We can thus conclude that all of the charge must reside at the surfaces of the sphere. If we now apply Gauss' law by taking a spherical closed surface that runs inside the metal, we find that the total charge contained inside that surface is zero. This means that the charge cannot reside on the inner surface.