GATE EC 2007 Electromagnetics Solution Q 3

GATE EC 2007 Electromagnetics Solution Q 3

A plane wave of wavelength λ is travelling in a direction making an angle 30 degree with positive x-axis and 90 degree with positive y-axis. The vector E field of the plane wave can be represented as (E0 is a constant)

(a) \overrightarrow E=\widehat yE_0e^{j\left(\omega t-\frac{\sqrt{3\pi}}\lambda x-\frac\pi\lambda z\right)}

(b) \overrightarrow E=\widehat yE_0e^{j\left(\omega t-\frac\pi\lambda x-\frac{\sqrt{3\pi}}\lambda z\right)}

(c) \overrightarrow E=\widehat yE_0e^{j\left(\omega t-\frac{\sqrt{3\pi}}\lambda x+\frac\pi\lambda z\right)}

(d) \overrightarrow E=\widehat yE_0e^{j\left(\omega t-\frac\pi\lambda x+\frac{\sqrt{3\pi}}\lambda z\right)}

Ans : a)

Explanation

As the wave is travelling along positive X-Z direction, the propagation constant should have negative x and z coefficients, so option (a) or (b) would be our choice.

But as the wave is making 30o with positive X axis option (a) is correct one.

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