Question

Show that the force on each plate of a parallel plate capacitor has a magnitude of ½QE. Where Q in charge on capacitor and E is the field between the plates

Answer 1

Here we can consider the capacitor plates as infinitely charged planes having uniform distributions.

now, the force of attraction on a plate of area A due to influence of another plate of equal area would be

F = σ²A / 2ε₀

or

F = (1/2).(σ/ε₀).(σA)

now, in this case we know that

E = σ/ε₀

Q = σA

thus,

F = (1/2).E.Q

or

F = (1/2)QE