Which current flows inside a capacitor when it is being charged? Explain.

(N/A) When a capacitor is being charged, the current flowing inside the capacitor is known as the $displacement \ current$ $(I_d)$.
Explanation:
$1$. In the conducting wires connected to the capacitor plates, the current is the $conduction \ current$ $(I_c)$, which is due to the actual flow of electrons.
$2$. Between the plates of the capacitor, there is no physical medium for electrons to flow, so the $conduction \ current$ is zero.
$3$. However, as the capacitor charges, the electric field $(E)$ between the plates changes with time.
$4$. According to Maxwell's modification of Ampere's Law, this time-varying electric field produces a magnetic field, which is equivalent to a current.
$5$. This current is defined as $I_d = \epsilon_0 \frac{d\Phi_E}{dt}$, where $\epsilon_0$ is the permittivity of free space and $\frac{d\Phi_E}{dt}$ is the rate of change of electric flux.
$6$. Thus, the $displacement \ current$ ensures the continuity of the total current in the circuit.