Question

A plane electromagnetic wave is propagating along the direction $\frac{\hat{i}+\hat{i}}{\sqrt{2}},$ with its polarization along the direction $\hat{k}.$ The correct form of the magnetic field of the wave would be (here $B_0$ is an appropriate constant):

• A. $B_0\frac{\hat{i}-\hat{j}}{\sqrt{2}}cos\left(\omega t-k\frac{\hat{i}+\hat{j}}{\sqrt{2}}\right)$
• B. $B_0\frac{\hat{j}-\hat{i}}{\sqrt{2}}cos\left(\omega t-k\frac{\hat{i}+\hat{j}}{\sqrt{2}}\right)$
• C. $B_0\frac{\hat{i}+\hat{j}}{\sqrt{2}}cos\left(\omega t-k\frac{\hat{i}+\hat{j}}{\sqrt{2}}\right)$
• D. $B_0\hat{k}cos\left(\omega t-k\frac{\hat{i}+\hat{j}}{\sqrt{2}}\right)$

Answer 1

Answer: (A)

Direction of polarisation $=\hat{E}=\hat{k}$
Direction of propagation $=\hat{E}\times \hat{B}=\frac{\hat{i}+\hat{j}}{\sqrt{2}}$
$\therefore \hat{E}\times \hat{B}=\frac{\hat{i}+\hat{j}}{\sqrt{2}}$
$\hat{B}=\frac{\hat{i}+\hat{j}}{\sqrt{2}}$