Working with the electric field between 2 parallel plates

Imagine to circular flat plates of radius R that are separated by a small distance s. Imagine that we connect the plates to a power supply that puts opposite charges on the plates of whatever magnitude Q is necessary to set up a fixed potential difference (delta*sigma) between them.

A) argue that the magnitude of the total force that each plate exerts on the other is given by

F=2(pi)kQ^2/A where A is the area of each plate. What assumptions do you have to make?

B) show that you can eliminate the unknown charge Q from this expression to get

F=(1/8k)(R*delta*sigma/s)^2

Solution Preview

The electric field E due to a charged sheet is given by the equation

E = surface charge density/(2* epsilon_0)

This can be very easily derived from Gauss's law (refer to Example 4 chapter 2 section 2.2.3 of Introduction to electrodynamics by David J Griffiths second edition)

Surface ...

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