Question

Calculate the electric potential V(h) inside the capacitor as a function of height h. Take the potential at the bottom plate to be zero.Express V(h) in terms of E and h.V(h) =

Answer 1

V(h) = Eh

Step-by-step explanation:

I will assume that the capacitor is a parallel-plate capacitor.

By Gauss' Law, electric field inside the capacitor is

`E = (\sigma)/(\epsilon_0) = (Q)/(\epsilon_0 A)`

The relation between electric field and potential is

`V_(ab) = -\int\limits^b_a {\vec{E}(h)} \, d\vec{h}  = \int\limits^h_0 {(Q)/(\epsilon_0 A)} \, dh \\V(h) - V(0) = V(h) - 0 = Eh\\V(h) = Eh`

The important thing in this question is that the electric field inside the parallel plate is constant. So, the potential is also constant and proportional to the distance, h.