Answer to Question #71201 in Electric Circuits for Mehdi

Question

hi is it possible to calculate the force between two parallel plates?

Answer 1

If the plates carry equal but opposite charges, the force of attraction, which is conservative, is given by

F=-∂W/∂x.

But

W=q^2/2C.

For the parallel plate capacitor,

C=(ε_0 S)/x,

where x is the distance of separation. So

F=-d/dx ((q^2 x)/(2ε_0 S))=-q^2/(2ε_0 S)=-(ε_0 SU^2)/(2d^2 ),

where we have put x=d and q=CU.

Answer. F=-(ε_0 SU^2)/(2d^2 ).