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

Answer:

V(h) = Eh

Explanation:

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

By Gauss' Law, electric field inside the capacitor is

$E = \frac{\sigma}{\epsilon_0} = \frac{Q}{\epsilon_0 A}$

The relation between electric field and potential is

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

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.