GATE EC 2004 Electromagnetics Solution Q 1

GATE EC 2004 Electromagnetics Solution Q 1

A parallel plate air-filled capacitor has plate area of 10^{-4}\;\;m^2 and plate separation of 10^{-3}m It is connected to a 0.5 V, 3.6 GHz source. The magnitude of the displacement current is \left(\varepsilon_0=1/36\pi\times10^{-9}F/m\right)

a) 10 mA

b) 100 mA

c) 10 A

d) 1.59 mA

Ans- a)

Explanation

Displacement Current density is given as,

{\overline J}_{disp}=\frac{\partial\overline D}{\partial t} \begin{array}{l}I_d=AJ_d\\\;\;\;=A\frac{\partial D}{\partial t}=A\in\frac{\partial E}{\partial t}\end{array} \left|I_d\right|=\left|A\in\omega E\right|=A\omega\in\frac Vd

Solving we get,

I_d=10mA

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