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
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)
The solution gives all steps along with proper explanations so that you can solve similar problems yourself.