Question

An electromagnetic wave travels in vacuum along $z$ direction: $E=\left(E_1\hat{i}+E_2\hat{j}\right)\cos (kz-\omega t)$. Choose the correct options from the following

• A. The associated magnetic field is given as $B=\frac{1}{c}\left(E_1\hat{i}+E_2\hat{j}\right)\cos (kz-\omega t)$
• B. The associated magnetic field is given as $B=\frac{1}{c}\left(E\hat{i}-E_2\hat{j}\right)\cos (kz-\omega t)$
• C. The given electromagnetic field is circularly polarised
• D. The given electromagnetic wave is plane polarised

Answer 1

Answer: (A), (D)

In electromagnetic wave, the electric field vector is given as,
$E=\left(E_1\hat{i}+E_2\hat{j}\right)\cos (kz-\omega t)$
In electromagnetic wave, the associated magnetic field vector,
$B=\frac{E}{C}=\frac{\left(E_1\hat{i}+E_2\hat{j}\right)}{C}\cos (kz-\omega t)$
As $E$ and $B$ are perpendicular to each other and the propagation of electromagnetic wave is perpendicular to $E$ as well as $B$, so the given electromagnetic wave is plane polarised.