JEE PYQ: Electromagnetic Waves Question 16
Question 16 - 2020 (04 Sep 2020 Shift 2)
The electric field of a plane electromagnetic wave is given by $\vec{E} = E_0 (\hat{x} + \hat{y}) \sin(kz - \omega t)$. Its magnetic field will be given by:
(1) $\frac{E_0}{c}(-\hat{x} + \hat{y}) \sin(kz - \omega t)$
(2) $\frac{E_0}{c}(\hat{x} + \hat{y}) \sin(kz - \omega t)$
(3) $\frac{E_0}{c}(\hat{x} - \hat{y}) \sin(kz - \omega t)$
(4) $\frac{E_0}{c}(\hat{x} - \hat{y}) \cos(kz - \omega t)$
Show Answer
Answer: (1)
Solution
Direction of propagation $= +\hat{k}$. $\hat{k} = \frac{(\hat{i} + \hat{j})}{\sqrt{2}} \times \hat{B}$, so $\hat{B} = \frac{-\hat{i} + \hat{j}}{\sqrt{2}}$. $\vec{B} = \frac{E_0}{c}(-\hat{x} + \hat{y})\sin(kz - \omega t)$.
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