Electrostatics : A parallel plate capacitor with a partial dielectric

Problem statement

Consider a parallel plate capacitor which is only partially filled with a slab of dielectric, the remaining thickness being made up of air.

Objective : to find the capacitance C between the plates given the thickness of the dielectric.
Principles : Gauss' law.

Method of analysis :	1) define the potential difference V between the plates,
			2) define the magnitude of the charge per unit area [sigma] on the plates.

Sketch :

Maths :

Matlab(R) solution
Solution variables
Input variables



Charge on plate q (coulombs)			
Air thickness t1 (metres)			
Dielectric thickness, t2 (metres)		
Area of capacitor plates A (metres sq.)		
Relative permittivity of the dielectric, er 	



Output variables


Electric field strength, E
Potential difference between the plates, V
Capacitance , C