electromagnetics

I am reading Sadiku's Elements of Electromagnetics and here is the proof given to show that conduction current = displacement current for parallel-plate capacitor. Displacement current: \begin{align*} E &= \frac{V}{d}\\ D &= \epsilon E = \epsilon \frac{V}{d}\\ J_d &= \frac{\partial D}{\partial t} = \frac{\epsilon}{d}\frac{dV}{dt}\\ I_d &= J_d \cdot S = \frac{\epsilon S}{d}\frac{dV}{dt} = C\frac{…