An electromagnetic wave travelling along z-axis is given as $\vec{E} = {\vec{E}}_{o} \cos (k z - w t) (- \hat{j})$ . Choose the wrong option from the following

Moderate

A

The associated magnetic field is given as $\vec{B} = \frac{1}{C} (\hat{k} \times \vec{E})$
B

The electromagnetic field can be written in terms of the associated magnetic field as $\vec{E} = C (\vec{B} \times \hat{k})$
C

$\hat{k} . \vec{E} = 0, \hat{k} . \vec{B} = 0$
D

$\hat{k} \times \vec{E} = 0, \hat{k} \times \vec{B} = 0$

Solution

Suppose an electromagnetic wave is travelling along negative z-direction. Its electric field is given by $\vec{E} = {\vec{E}}_{o} \cos (k z - w t) (- \hat{j})$ which is perpendicular to Z-axis. It acts along negative y-direction
The associated magnetic field in electromagnetic wave is along positive x-axis, i.e, along $(\hat{k} \times \vec{E})$ . As $B_{o} = \frac{E_{o}}{C} ∴ \vec{B} = \frac{1}{C} (\hat{k} \times \vec{E})$
So, option 1 is correct
The associated electric field can be written in terms of magnetic field as $\vec{E} = C (\vec{B} \times \hat{k})$ . So, option 2 is correct
Angle between $\hat{k}$ and $\vec{E}$ is $90^{0}$ and between $\hat{k}$ and $\vec{B}$ is $90^{0}$ . So option 3 is correct

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