A plane wave has E(z,t)=3 x( t-kz+30)-4 y( t-kz+45) mV/m. Find its polarization.

GATE 2014 EC (EC2) – Question 63

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

A plane wave has $\mathbf E(z,t)=3\hat x\cos(\omega t-kz+30^\circ)-4\hat y\sin(\omega t-kz+45^\circ)$ mV/m. Find its polarization.

Left elliptical
Left circular
Right elliptical
Right circular

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (A) Left elliptical

Explanation

Rewrite Ey=−4sin(ψ+45°)=4cos(ψ+135°), while Ex=3cos(ψ+30°), with ψ=ωt−kz. The components have unequal amplitudes and a105°phase difference, so the polarization is elliptical. At the positive Ex maximum, Ey is decreasing; the vector turns toward negative y. In the propagation-view antenna convention used by the official key this is **left elliptical,A**.