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)

$B_{0} \frac{\hat{i}-\hat{j}}{\sqrt{2}}cos \left(\omega t-k \frac{\hat{i}+\hat{j}}{\sqrt{2}}\right)$

Answer 2

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