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

Understanding Displacement Current and Continuity in a Charging Capacitor 
 

1: Definition of Displacement Current
- The displacement current (\( I_d \)) is a term introduced by James Clerk Maxwell to explain how a changing electric field can produce a magnetic field, similar to a conduction current.
- It is given by: \[ I_d = \epsilon_0 \frac{d\Phi_E}{dt} \] where:
- \( \epsilon_0 \) = Permittivity of free space,
- \( \Phi_E \) = Electric flux through a given surface.
2: Continuity of Current in a Charging Capacitor
- Consider a capacitor connected to a DC source.
- During charging, conduction current flows in the wires.
- Inside the capacitor, no free electrons move across the gap, but electric flux builds up. \[ I_d = \epsilon_0 \frac{d\Phi_E}{dt} \] - Maxwell’s Equation states that displacement current maintains continuity, ensuring a continuous magnetic field around the circuit.
- Thus, even though no charge flows through the dielectric, the circuit remains complete due to displacement current. 
3: Conclusion
- Displacement current is required to modify Ampère’s Law and explain how a capacitor circuit remains continuous even in the absence of conduction current in the capacitor gap.