An electromagnetic wave travelling along

Question:

An electromagnetic wave travelling along the z-axis is given as: E = E0 cos (kz – ꞷt). Choose the correct options from the following

(a) the associated magnetic field is given as

$B=\frac{1}{c} \hat{k} \times E=\frac{1}{\omega}(\hat{k} \times E)$

(b) the electromagnetic field can be written in terms of the associated magnetic field as

$E=c(B \times \hat{k})$

(c)

$\hat{k} \cdot E=0, \hat{k} \cdot B=0$

(d)

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

Solution:

(a) the associated magnetic field is given as

$B=\frac{1}{c} \hat{k} \times E=\frac{1}{\omega}(\hat{k} \times E)$

(b) the electromagnetic field can be written in terms of the associated magnetic field as

$E=c(B \times \hat{k})$

(c)

$\hat{k} \cdot E=0, \hat{k} \cdot B=0$