Electrostatics : A parallel plate capacitor with dielectric

Problem statement

Consider a parallel plate capacitor with a partially inserted dielectric. The dielectric will become polarised by the electric field between the capacitor plates. At the edge of the dielectric the electric field lines bend as shown in the sketch, and exert a force tending to pull the dielectric slab into the capacitor.

Objective : to find the force exerted on the dielectric F due to the applied voltage.
Principles : Virtual Work.

Method of analysis : Energy balance.

Sketch :

Maths :

Matlab(R) solution
Solution variables
Input variables



Applied voltage, V (volts)				
Depth of plates, h (metres)				
Length of plates, d (metres)				
Thickness of the dielectric, t (metres)			
Distance of dielectric into plates, X (metres)		
Relative permittivity of the inner dielectric, er 	



Output variables


Force, F
Capacitance, C