Magnetism And Maxwell S Equations

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: