JEE Main 2025 — Electromagnetic Waves Question with Solution

To determine the displacement current through a hypothetical plane surface within a parallel plate capacitor, follow these steps:

Current Density Calculation:

The current density ($J_d$) is the current ($I$) divided by the area ($A$) of the capacitor plates.

Given: $I=6\text{A}$ and $A=16{\text{cm}}^2$.

$J_d=\frac{I}{A}=\frac{6\text{A}}{16{\text{cm}}^2}$

Displacement Current Through the Hypothetical Surface:

The hypothetical surface has an area $A_0=3.2{\text{cm}}^2$.

The displacement current through this smaller area ($I_{small}$) is the current density multiplied by the area of the hypothetical surface.

$I_{small}=J_d\times A_0=\frac{6\text{A}}{16{\text{cm}}^2}\times 3.2{\text{cm}}^2$

Calculation:

Simplify the expression to find the displacement current:

$I_{small}=\left(\frac{6}{16}\right)\times 3.2=1.2\text{A}=1200\text{mA}$

Thus, the displacement current through the hypothetical plane surface is 1200 mA.