Question #43252

This question tests the fundamental definition of displacement current in the presence of a dielectric.

A common misconception among students is to define displacement current solely as $I_d = \epsilon_0 \frac{d\Phi_E}{dt}$ (the vacuum term), ignoring the contribution of the polarization current $I_p = \frac{d\Phi_P}{dt}$.

In this scenario, the electric field $E$ is constant because the applied voltage $V_0$ is constant, which leads students to incorrectly conclude that the displacement current and the induced magnetic field are zero (Option B).

However, the true source of the Maxwell-Ampere magnetic field is the total displacement current density $J_d = \frac{\partial D}{\partial t} = \epsilon_0 \frac{\partial E}{\partial t} + \frac{\partial P}{\partial t}$.

The time-varying dielectric constant creates a non-zero polarization current $\frac{\partial P}{\partial t}$, which drives the magnetic field even when the macroscopic electric field is strictly static.