Point charge between two conducting plates

[-marko-]

Two infinite conducting plates 1 and 2 are separated by a distance l. A point charge q is located between the plates at a distance x from plate 1. Find the charges induced on each plate.

I solved this problem assuming (intuitively) that a potential difference between plate 1 and 2 equals 0 and got correct result but I don't understand why is that correct assumption when two plates are not connected with conductor? I also imagined that charge q is uniformly spread over the plane passing through that charge and parallel to the plates because induced charge remains unchanged if we imagine this.

Thanks

 

[Astronuc]

I solved this problem assuming (intuitively) that a potential difference between plate 1 and 2 equals 0 and got correct result but I don't understand why is that correct assumption when two plates are not connected with conductor?

If both plates are electrically neutral, i.e. there is no net excess or deficiency of electrons, they must be by definition at the same electrical potential. Attaching a conductor would ensure the same electric potential regardless of the free charges.

I also imagined that charge q is uniformly spread over the plane passing through that charge

But that is a point charge, not a distribution of charge.

The charge q has an electric field associated with it. It is this electric field which induces a redistribution of charge on the conductor.

 

[Meir Achuz]

Two infinite conducting plates 1 and 2 are separated by a distance l. A point charge q is located between the plates at a distance x from plate 1. Find the charges induced on each plate.

I solved this problem assuming (intuitively) that a potential difference between plate 1 and 2 equals 0 and got correct result but I don't understand why is that correct assumption when two plates are not connected with conductor? I also imagined that charge q is uniformly spread over the plane passing through that charge and parallel to the plates because induced charge remains unchanged if we imagine this.

Thanks

If the plates are isolated, they can't have any charge induced on them.
Where would it come from? That problem is usually given for grounded planes.

Your assumption may give the right answer, but it is difficult to justify.
The problem is usually given as an example of the use of Green's reciprocity theorem.