Question

A parallel - plate capacitor is being charged.Show that the displacement current across an area in the region between the plates and parallel to it is equal to the conduction current in the connecting wires.

Answer 1

P1 and P2 are plates of capacitor. Conduction current going to plates is i.

1. Field across region between plates $E= \frac{Q}{E. A }$
2. Flux= Q/∈
3. Displacement current= ∈ {d∅/dt}
4. ∴ Displacement current= ∈ d/dt{Q/∈}

                                             =dQ/dt

But, rate of change of charge at a plate is conduction current.

Conduction current= dQ/ dt

Hence, we see that displacement current is equal to conduction current.

Answer 2

To show the displacement current is same as the capacitor current.

• The displacement current is represented by I
• The formula of displacement current using the maxwell's equation.
• I=ε₀dФ/dt
• Now using the conduction current formula
• Ic=dq/dt
• Now the Gauss theorem

• Ф=q/ε₀
• Put back these value in above equation

• We get I=dq/dt
• This shows that the displacement current is equal to the conduction current flowing in the circuit.