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.
You have two questions. One is "what is the charge distribution on a non symmetric conductor" and the other is "how can the inner surface of a conductor be charged?"
Q1:
The charges will distribute themselves in a manner to minimize total energy (whenever you don't know an answer on the exam, say that ;). Since it's a conductor, they will distribute themselves in such a way that the potential anywhere on the surface is the same (otherwise, the charges would have a gradient they could move along).
Q2
Assumptions:
Let's assume electro statics i.e. no time dependence, and perfect conductors.
Also let's assume the tubes are infinitely long. Therefore, this becomes a 2D problem of concentric circles (senior electromagnetis becomes much simpler when you realize they only ever test you on a handful of geometries).
Solution:
Point 1) The electric field inside a perfect conductor is zero (otherwise a current would arise, rearranging the charge until the field is cancelled out). Therefore, within the material of the thin outer tube, the electric field is zero.
Point 2) However, the integral of the electric field along a path (it's a path integral because we're in 2D!) is equal to the enclosed charge (Gauss' law). From symmetry, there is no angular dependence.
Conclusion) The only way for the first point and the second point to be both correct is if you have a charge in the inner surface of the tube. The charge on the inner surface of the tube needs to cancel out the electric field from the rod, so it is equal and opposite to the charge of the rod. The outer surface also has a charge, equal to the net charge of the tube minus the charge on the inner surface of the tube.
Remember:
The fundamental rule of a conductor is that the electric field within it is zero. There's no fundamental rule against charges on the inside surface of a conductor!
Further investigation:
Realistically charges are electrons in thermal equilibrium. How does this affect our mental image of "charges on an infinitely thin surface"?
Best Answer
If the "excess charges" are in a conductor then they are, by definition, free to move. If there are excess charges distributed throughout the conductor then they will be compelled to move by any electric field within the conductor.
Gauss's law tells us that if there is any net free charge within the conductor then this also produces an electric field within the conductor. The electric field will cause the charges to move, and they will do so until this electric field is zero. Gauss's law then also tells us that this will be accomplished once there is no net free charge within the conductor, so the free charge must accumulate on the surface.