Question 168: EM waves

Question

A parallel plate capacitor of area $A=16 \mathrm{~cm}^2$ 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 .

Accepted Answer

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 \, 	ext{A} $ and $ A = 16 \, 	ext{cm}^2 $.
$    J_d = \frac{I}{A} = \frac{6 \, 	ext{A}}{16 \, 	ext{cm}^2}    $
Displacement Current Through the Hypothetical Surface
:
The hypothetical surface has an area $ A_0 = 3.2 \, 	ext{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 	imes A_0 = \frac{6 \, 	ext{A}}{16 \, 	ext{cm}^2} 	imes 3.2 \, 	ext{cm}^2    $
Calculation
:
Simplify the expression to find the displacement current:
$    I_{small} = \left(\frac{6}{16}ight) 	imes 3.2 = 1.2 \, 	ext{A} = 1200 \, 	ext{mA}    $
Thus, the displacement current through the hypothetical plane surface is 1200 mA.

EM waves

Integer / Numeric Answer Type