Question

What is meant by displacement current? How is this current different from the conduction current? A capacitor is being charged by a source of emf. Justify the continuity of current in the circuit.

Hint:

The displacement current allows capacitor circuits to obey Kirchhoff’s laws by ensuring a continuous current flow in the circuit, even though no actual charge moves across the capacitor plates.

Answer 1

Displacement Current and Continuity in a Charging Capacitor

1: Displacement Current Definition
- James Clerk Maxwell introduced displacement current (\( I_d \)) to describe how a changing electric field generates a magnetic field, analogous to conduction current.
- The formula is: \[ I_d = \epsilon_0 \frac{d\Phi_E}{dt} \]
- Here,
- \( \epsilon_0 \) denotes the permittivity of free space.
- \( \Phi_E \) represents the electric flux through a specific surface.
2: Current Continuity in a Charging Capacitor
- When a capacitor is connected to a DC source,
- Conduction current flows in the wires during charging.
- Within the capacitor, although no free electrons traverse the gap, electric flux increases.
\[ I_d = \epsilon_0 \frac{d\Phi_E}{dt} \]
- Maxwell’s Equation posits that displacement current ensures continuity, thereby maintaining a continuous magnetic field around the circuit.
- Consequently, the circuit remains complete despite the absence of conduction current through the dielectric.
3: Summary
- Displacement current is essential for modifying Ampère’s Law, explaining the continuity of a capacitor circuit even without conduction current in its gap.