A parallel plate capacitor of area $\mathrm{A}=16 \mathrm{~cm}^{2}$ and separation between the plates 10 cm , is charged by a DC current. Consider a hypothetical plane surface of area $\mathrm{A}_{0}=3.2 \mathrm{~cm}^{2}$ inside the capacitor and parallel to the plates. At an instant, the current through the circuit is 6A. At the same instant the displacement current through $\mathrm{A}_{0}$ is ______ mA .

JEE Main · 2025 · 22 Jan 2025 · Shift 2 · EM Waves

A parallel plate capacitor of area

A = 16 cm^{2}

and separation between the plates 10 cm , is charged by a DC current. Consider a hypothetical plane surface of area

A_{0} = 3.2 cm^{2}

inside the capacitor and parallel to the plates. At an instant, the current through the circuit is 6A. At the same instant the displacement current through

A_{0}

is ______ mA .

Answer: 1200

Solution

The displacement current density between the plates is uniform and equals the conduction current divided by the plate area:

J_{d} = \frac{I}{A} = \frac{6}{16} A/cm^{2}

The displacement current through the smaller surface of area

A_{0}

I_{d} = J_{d} \times A_{0} = \frac{6}{16} \times 3.2 = 1.2 A = 1200 mA

JEE Main · 2025 · 22 Jan 2025 · Shift 2 · Integer answer

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