Question

Differentiate between conduction current and displacement current. A capacitor is connected across a source providing time-dependent current. Explain how the total current at an instant is the sum of conduction current and displacement current in the circuit at that instant.

Hint:

Displacement current is the "missing link" that allowed Maxwell to predict the existence of electromagnetic waves.

Answer 1

Step 1: Understanding the Concept:
To maintain the continuity of current in a circuit containing a capacitor, Maxwell introduced the concept of displacement current, which exists in regions where the electric flux is changing with time.

Step 2: Detailed Explanation:
Differentiation:

Conduction Current (\(I_c\)): Current due to the actual flow of electrons through a conductor (wires).
Displacement Current (\(I_d\)): Current that arises due to a changing electric field between the plates of a capacitor. It is given by \(I_d = \epsilon_0 \frac{d\Phi_E}{dt}\).
Total Current Continuity: In a capacitor circuit, \(I_c\) flows through the connecting wires but cannot cross the vacuum/dielectric gap between the plates. However, as the plates charge up, the electric field between them changes. This changing field creates a displacement current \(I_d\) that is exactly equal to \(I_c\). Maxwell’s Ampere Law states the total current \(I\) is: \[ I = I_c + I_d \] Outside the plates, \(I_d = 0\), so \(I = I_c\). Between the plates, \(I_c = 0\), so \(I = I_d\). This ensures the current is continuous throughout the circuit.

Step 3: Final Answer:
Conduction current is due to charge flow, while displacement current is due to changing electric flux. The total current is \(I = I_c + \epsilon_0 \frac{d\Phi_E}{dt}\).