Question

Two very large slabs of metal are placed parallel to each other and are at a small distance apart from one another. One plate has a 2Q charge on it and the other has a 3Q charge on it. You may assume that the thickness of each slab is so small in comparison to its lateral dimensions that the surface area around the sides is negligible.

a) How are charges 2Q and 3Q distributed?

b) State the formula for the magnitude of the field between these two parallel slabs of metal.

c) State the formula for the field between any two very large slabs of metal that are parallel to each other.

Answer 1

a. The charges 2Q and 3Q will be evenly distributed over the whole surface following a surface charge density value different for both the cases. We can assume these to be sigma1 and sigma2 for both slabs respectively.

b. By using gausses law and the aforementioned charge densities we have:

Now, electric field due to a surface charge distribution is given by

Now since both these charges are of same kind we have:

Since, both the slabs are of very large surface areas we can assume

The negative sign indicates the direction of the field.

c. For this case we will consider the equation stated above which has a more general form: