Electromagnetic Waves

JEE Main level, single correct, medium

123 of 165

Question 123 of 165

For plane electromagnetic waves propagating in the +z+z-direction, which one of the following combinations gives the correct possible direction for E⃗\vec{E} and B⃗\vec{B} field respectively?

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Answer: (B) (−2i^−3j^)\left(-2\hat{i}-3\hat{j}\right) and (3i^−2j^)\left(3\hat{i}-2\hat{j}\right)

The direction of propagation of the electromagnetic waves is along E⃗×B⃗\vec{E}\times \vec{B}.

Also E⃗⋅B⃗=0\vec{E}\cdot \vec{B}=0

When E⃗\vec{E} is along −2i^−3j^-2\hat{i}-3\hat{j}

And B⃗\vec{B} is along 3i^−2j^3\hat{i}-2\hat{j}

Then E⃗×B⃗=(−2i^−3j^)×(3i^−2j^)\vec{E}\times \vec{B}=\left(-2\hat{i}-3\hat{j}\right)\times \left(3\hat{i}-2\hat{j}\right)

=4k^+9k^=4\hat{k}+9\hat{k}

=13k^=13\hat{k} is along +ve direction also E⃗⋅B⃗=0\vec{E}\cdot \vec{B}=0

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