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.
 A: 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.


See http://www.physlink.com/education/askexperts/ae28.cfm

 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.
A: 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.
A: 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.
A: 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.
