# Force on charges inside/out of a hollow conductor

• wizang
In summary, the conversation discusses a situation where two charges, q and q', are located inside and outside a hollow conductor. It is explained that q' experiences a force due to q, but not vice versa. This apparent violation of Newton's third law is then proven by considering the presence of a neutralizing electric field within the conductor. It is also mentioned that the conversation delves into the difficulty of conceptual problems in electromagnetism and the need for conservation laws to prove certain phenomena.

## Homework Statement

Two charges, q and q', are located respectively, inside and outside a hollow conductor. Charge q' experiences a force due to q, but not vice versa. Prove this statement and explain the apparently violation of Newton's third law. There is no net charge on the conductor.

## Homework Equations

None really, conceptual problem.

## The Attempt at a Solution

I always have a hard time with E+M conceptual problems in particular for some reason. I'll muddle my way through an explanation, feel free to correct/ridicule or whatever. For example, let's say the charge inside the conductor is negative, and the charge outside is positive. The inner charge with induce a positive charge on the inner surface of the conductor, and a positive charge on the outside. The outer charge will feel a force due to the negative charge on the conductor due to the inner charge. Here's where I feel less confident. I think of the inner charge being sort of "shielded" against the outer charge since there is a positive charge on the inside of the conductor. The outer charge is exerting a force on the conductor then rather than the inner charge. I can't really explain how this is okay under the third law, any hints? Thank you very much.

I was waiting for someone else to help, but as there don't seem to be any other volunteers ...

OK, it's obvious why there should be an electeric field at q'. Just invoke the Gauss theorem.

The E field inside the sphere (where q is located) is zero, because charge on the (outer)surface moves towards q' and away from the opposite direction, away from q'. This sets up a neutralizing field within the sphere such that the net field is zero.

Of course, the force is on the sphere in lieu of being on q, so ole' Isaac is not violated.

I have tried to prove this rigorously but can't think of a way to do that. There must be some conservation law that can prove it.

## 1. How is the force on a charge inside a hollow conductor different from the force on a charge outside?

The force on a charge inside a hollow conductor is zero, while the force on a charge outside is non-zero. This is because the charges inside the conductor are evenly distributed and cancel out each other's electric fields, resulting in a net electric field of zero inside the conductor.

## 2. What is the direction of the force on a charge inside a hollow conductor?

The force on a charge inside a hollow conductor is always perpendicular to the surface of the conductor. This is because the electric field inside the conductor is zero, so there is no electric force acting in the direction of the field.

## 3. Does the size of the hollow conductor affect the force on a charge inside?

No, the size of the hollow conductor does not affect the force on a charge inside. As long as the charge is inside the conductor, the force will always be zero. However, the shape of the conductor can affect the direction of the force on the charge.

## 4. How does the presence of other charges affect the force on a charge inside a hollow conductor?

The presence of other charges outside the conductor has no effect on the force on a charge inside. This is because the charges inside the conductor are shielded from external electric fields due to the conductor's surface.

## 5. Can the force on a charge inside a hollow conductor ever be non-zero?

No, the force on a charge inside a hollow conductor can never be non-zero. This is because the charges inside the conductor are free to move and will always distribute themselves in a way that cancels out any external electric fields, resulting in a net electric field of zero inside the conductor.