Step 1: Understanding the Concept:
Displacement current is a quantity appearing in Maxwell's equations that is defined in terms of the rate of change of electric flux.
Inside the gap of a capacitor, there is no physical flow of electrons (conduction current), yet a magnetic field is produced when the capacitor is charging or discharging.
James Clerk Maxwell introduced the concept of displacement current to explain this phenomenon and satisfy the continuity of current.
Step 2: Key Formula or Approach:
Displacement current (\(I_d\)):
\[ I_d = \epsilon_0 \frac{d\Phi_E}{dt} \]
where \(\Phi_E\) is the electric flux. For a capacitor, \(\Phi_E = EA = \frac{V}{d} A\).
\[ I_d = \epsilon_0 \frac{A}{d} \frac{dV}{dt} = C \frac{dV}{dt} \]
Step 3: Detailed Explanation:
From the expression \(I_d = C \frac{dV}{dt}\), it is clear that for displacement current to be non-zero, the rate of change of voltage with respect to time must be non-zero.
Step A: If the voltage is increasing (\(dV/dt>0\)), \(I_d \neq 0\). This occurs during charging.
Step B: If the voltage is decreasing (\(dV/dt<0\)), \(I_d \neq 0\). This occurs during discharging.
Step C: If the voltage is constant (\(dV/dt = 0\)), then \(I_d = 0\). (Attaining a constant value leads to zero displacement current).
Step D: If the voltage is zero and stays zero, no current flows.
Thus, displacement current exists as long as the electric field (and thus voltage) across the capacitor plates is changing.
Step 4: Final Answer:
Displacement current is a transient effect proportional to the time derivative of the electric field. It flows when the voltage is either increasing or decreasing.