A plane electromagnetic wave is propagating along the direction i ^ + j ^ 2 , with its polarization along the direction k . ^ The correct form of the magnetic field of the wave would be (here B 0 is a

Question

A plane electromagnetic wave is propagating along the direction i ^ + j ^ 2 , with its polarization along the direction k . ^ The correct form of the magnetic field of the wave would be (here B 0 is an appropriate constant):

TestHub · Accepted Answer

Polarization of EM Wave means Direction of Its electric Field

Electric field vector is along $\hat{k}$

So, unit electric filed vector, $\vec{E} = \hat{k}$ (Given)

Direction of wave, $\hat{c} = \frac{\hat{i} + \hat{j}}{\sqrt{2}}$ (Given)

$\hat{B}$ denotes unit magnetic field vector.

$\hat{B} = \hat{C} \times \hat{E}$

$\hat{B} = \frac{\hat{i} + \hat{j}}{\sqrt{2}} \times \hat{k} = \frac{\hat{i} - \hat{j}}{\sqrt{2}}$

General Form is $B = (B_{0} \hat{B}) \cos (ω t - \hat{c} k)$

where $B_{0}$ is Magnitude of Magnetic Field

$S o, B = B_{0} \frac{\hat{i} - \hat{j}}{\sqrt{2}} \cos (ω t - k \frac{\hat{i} + \hat{j}}{\sqrt{2}})$

Physics - EM Waves Question with Solution | TestHub

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