Electromagnetic Waves

JEE Main level, single correct, medium

95 of 165

Question 95 of 165

In a plane electromagnetic wave, the directions of electric field and magnetic field are represented byk^\hat{k} and 2i^−2j^2\hat{i}-2\hat{j}, respectively. What is the unit vector along direction of propagation of the wave.

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Answer: (A) 12(i^+j^)\dfrac{1}{\sqrt{2}}(\hat{i}+\hat{j})

E⃗×B⃗‖C⃗\vec{E}\times \vec{B}‖\vec{C}
E^×B^=12∣i^j^k^0011−10∣=i^+j^2⇒c^=i^+j^2\hat{E}\times \hat{B}=\dfrac{1}{\sqrt{2}}\left|\begin{matrix}\hat{i} & \hat{j} & \hat{k} \\ 0 & 0 & 1 \\ 1 & -1 & 0\end{matrix}\right|=\dfrac{\hat{i}+\hat{j}}{\sqrt{2}}\Rightarrow \hat{c}=\dfrac{\hat{i}+\hat{j}}{\sqrt{2}}

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