The GATE Grind

GATE 2023 EC – Question 53

Electromagnetics · Plane Waves and Properties · 2 marks · Multiple select

The electric field of a plane electromagnetic wave is

$$\boldsymbol E=\boldsymbol a_xC_{1x}\cos(\omega t-\beta z)+\boldsymbol a_yC_{1y}\cos(\omega t-\beta z+\theta)\quad\text{V/m}.$$

Which of the following combination(s) will give rise to a left handed elliptically polarized (LHEP) wave?

  1. $C_{1x}=1,\ C_{1y}=1,\ \theta=\pi/4$
  2. $C_{1x}=2,\ C_{1y}=1,\ \theta=\pi/2$
  3. $C_{1x}=1,\ C_{1y}=2,\ \theta=3\pi/2$
  4. $C_{1x}=2,\ C_{1y}=1,\ \theta=3\pi/4$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (A) $C_{1x}=1,\ C_{1y}=1,\ \theta=\pi/4$; (B) $C_{1x}=2,\ C_{1y}=1,\ \theta=\pi/2$; (D) $C_{1x}=2,\ C_{1y}=1,\ \theta=3\pi/4$

Explanation

For a wave travelling in $+z$, if $E_y$ leads $E_x$ in phase ($0<\theta<\pi$, i.e. $\sin\theta>0$) the field vector rotates from $+y$ towards $+x$, which is left-handed; if $E_y$ lags ($\pi<\theta<2\pi$) it is right-handed. Here $\sin(\pi/4)>0$ (A, elliptical because the axes are tilted), $\sin(\pi/2)>0$ (B), $\sin(3\pi/4)>0$ (D) are left-handed; $\sin(3\pi/2)<0$ (C) is right-handed.