Ncert Exercises & Solutions

An electromagnetic wave travels in a vacuum along the z-direction: \(E=\left(E_1 \hat{i}+E_2 \hat{j}\right) \cos (k z-\omega t)\). Choose the correct options from the following.

(a) The associated magnetic field is given as: \(E=\frac{1}{c}\left(E_1 \hat{i}+E_2 \hat{j}\right) \cos (k z-\omega t)\)
(b) The associated magnetic field is given as: \(E=\frac{1}{c}\left(E_1 \hat{i}-E_2 \hat{j}\right) \cos (k z-\omega t)\)
(c) The given electromagnetic field is circularly polarised.
(d) The given electromagnetic wave is plane polarised.

1. (b, c)

2. (a, c)

3. (a, d)

4. (c, d)

Given, \(\vec{E}=(E_2\hat{i}+E_2\hat{j})cos(kz-\omega t)\)
We know that, \(\vec{B}=\frac{\vec{E}}{c}\)
\(\Rightarrow \vec{B}= \frac{E_1 \hat{i}+E_2\hat{j}}{c} cos(kz-\omega t)\)
Also \(\vec{E}\) & \(\vec{B}\) are perpendicular to each other and the propagation of em-waves is perpendicular to \(\vec{E}\) as well as \(\vec{B},\) so the given em-wave is plane polarised.

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