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GATE 2020 EC – Question 55

Electromagnetics · Plane Waves and Properties · 2 marks · Numerical answer

The magnetic field of a uniform plane wave in vacuum is given by

$$\vec H(x,y,z,t)=(\hat a_x+2\hat a_y+b\,\hat a_z)\cos(\omega t+3x-y-z).$$

The value of $b$ is ________.

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Correct answer: 1

Explanation

The propagation vector is $\vec k=(3,-1,-1)$ (up to sign). For a uniform plane wave, $\vec H\perp\vec k$, so $(1,2,b)\cdot(3,-1,-1)=3-2-b=0$ and $b=1$.