Calculate Electrostatic Force Between Two Plates

[ak_47_boy]

Hello, first post here. I hope this is in the right section.
I have spent an hour or so surfing the net and could not figure this out (i am bad at physics).

How do you figure out the electrostatic force attracting two plates? The plates are 2sq/m, have a 0.006m spacing, and have 10000 volts of potential difference.

 

[Shooting Star]

Welcome. Since you said you were “bad” at Physics, I’m trying to give you a detailed solution.

When a voltage V is applied across the plates, suppose the plates receive charges +Q and -Q. The surface charge density on the plates are +s and –s, where s=Q/A. If the plates were infinite in extent, then each would produce an electric field of magnitude
s/(2e) = Q/(2Ae) --(1), where I’m writing e for epsilon_naught. Let d be the separation between the plates.

The sum of the fields of both the plates E = Q/(Ae) and V=E*d
=> Q = AeV/d --(2).

So, force on one plate due to field of other = Q*field = Q*Q/(2Ae) (from 1)
= eAV^2/(2d^2) (from 2).

Note that the electric field of each plate has been calculated for the case when each plate in infinite in extent. In practice, some correction factor is introduced.