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For a plane electromagnetic wave, the magnetic field at a point $x$ and time t is
$\vec{B} (x, t) = [1.2 \times 10^{- 7} \sin (0.5 \times 10^{3} x + 1.5 \times 10^{11} t) \hat{k}] T$
The instantaneous electric field $\vec{E}$ corresponding to $\vec{B}$ is ( speed of light $c = 3 \times 10^{8} m s^{- 1})$

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$\vec{E} (x, t) = [36 \sin (1 \times 10^{3} x + 0.5 \times 10^{11} t) \hat{j}] \frac{V}{m}$

$\vec{E} (x, t) = [36 \sin (0.5 \times 10^{3} x + 1.5 \times 10^{11} t) \hat{i}] \frac{V}{m}$

$\vec{E} (x, t) = [- 36 \sin (0.5 \times 10^{3} x + 1.5 \times 10^{11} t) \hat{j}] \frac{V}{m}$

$\vec{E} (x, t) = [36 \sin (0.5 \times 10^{3} x + 1.5 \times 10^{11} t) \hat{k}] \frac{V}{m}$

answer is C.

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Detailed Solution

$\begin{array}{l} E_{o} = c B_{o} = 36 \frac{V}{m} \\ \hat{E} = \hat{B} \times \hat{C} = \hat{k} \times (- \hat{i}) = - \hat{j} \end{array}$

Also E-field and B-field should be mutually perpendicular and have the same frequency and wavelength as they both represents the same wave.
Therefore correct key is option : 3

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