GATE EC 1991 Electromagnetics Solution Q 1

GATE EC 1991 Electromagnetics Solution Q 1

The electric field component of a uniform plane electromagnetic wave propagating in the Y-direction in lossless medium will satisfy the equation

(a) \frac{\partial^2E_y}{\partial y^2}=\mu\in\frac{\partial^2E_y}{\partial t^2}

(b) \frac{\partial^2E_y}{\partial x^2}=\mu\in\frac{\partial^2E_y}{\partial t^2}

(c) \frac{\partial^2E_x}{\partial y^2}=\mu\in\frac{\partial^2E_x}{\partial t^2}

(d) \frac{\sqrt{E_x^2+E_z^2}}{\sqrt{H_x^2+H_z^2}}=\sqrt{\mu/\in}

Ans : (c) and (d)

Explanation

As EM wave is propagating in Y- direction. E_y=H_y=0

So, \frac{\partial^2E_x}{\partial y^2}=\mu\in\frac{\partial^2E_x}{\partial t^2}

\frac{E_z}{H_x}=\eta \frac{E_x}{H_z}=-\eta \frac EH=\frac{\sqrt{E_x^2+E_z^2}}{\sqrt{H_x^2+H_z^2}}=\eta=\sqrt{\frac\mu\in}

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