Find the displacement current through a parallel-plate capacitor. Assume that V is the voltage across the capacitor at any instant. Express your answer in terms of the variables C and dV/dt.

displacement current; i_d = C (dV/dt)

Explanation:

Let i_d be the displacement current

Thus,

i_d = ε_o (dΦ/dt)

We know that flux Φ = EA

Thus,

i_d = ε_oA (dE/dt)

We also know that E = V/d

Thus, i_d = ε_oA (d (V/d) / dt)

i_d = ε_o (A/d) (dV/dt)

Now, capacitance has a formula of;

C = ε_o (A/d)

Thus,

i_d = C (dV/dt)