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