A plane electromagnetic wave of wavelength $λ$ has an intensity $I$ . It is propagating along the positive Y-direction. The allowed expression for electric and magnetic fields are given by:

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$\vec{E} = \sqrt{\frac{I}{ε_{0} c}} \cos [\frac{2 π}{λ} (y - ct)] \hat{i}; \vec{B} = \frac{1}{c} E \hat{k}$

$\vec{E} = \sqrt{\frac{2 I}{ε_{0} c}} \cos [\frac{2 π}{λ} (y + ct)] \hat{k}; \vec{B} = \frac{1}{c} E \hat{i}$

$\vec{E} = \sqrt{\frac{2 I}{ε_{0} c}} \cos [\frac{2 π}{λ} (y - ct)] \hat{k}; \vec{B} = \frac{1}{c} E \hat{i}$

$\vec{E} = \sqrt{\frac{I}{ε_{0} c}} \cos [\frac{2 π}{λ} (y - ct)] \hat{k}; \vec{B} = \frac{1}{c} E \hat{i}$

answer is C.

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Detailed Solution

If $E$ is magnitude of electric field, then:

$\frac{1}{2} ε_{0} E^{2} \times c = I$

$E = \sqrt{\frac{2 I}{{cε}_{0}}}$ and $B = \frac{E}{c}$

Also, the direction of $\vec{E} \times \vec{B}$ will be along $+ \hat{j}$ .

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