Concept:
Displacement current was introduced by Maxwell to explain continuity of current in circuits containing capacitors. It arises due to time-varying electric field, even where no charge flows physically.
Step 1: Definition of displacement current. Displacement current is defined as:
Where:
= permittivity of free space
= electric flux
Step 2: Charging capacitor case. When a capacitor is charging:
Conduction current flows in wires
No real charge flows across dielectric gap
But electric field between plates changes with time
Electric flux between plates:
As voltage increases, electric field changes:
Thus:
This ensures continuity:
Step 3: Conductor with constant voltage. For a conductor with constant applied voltage:
Electric field is constant
Electric flux does not change with time
So:
Hence:
Final Answers:
Displacement current:
For a conductor at constant voltage: