JEE Physics 2023 Question with Solution

Given: $\vec{E}$ is the electric field vector, $\vec{K}$ is the propagation vector, and $\omega$ is the angular frequency of an electromagnetic wave in vacuum.

Find: The correct expression for the magnetic field vector $\vec{B}$.

For an electromagnetic wave in vacuum, the electric field, magnetic field, and propagation direction are mutually perpendicular. The magnetic field direction is obtained from the cross product of the propagation vector and the electric field.

This also gives the correct vector direction because $\vec{K} \times \vec{E}$ is perpendicular to both $\vec{K}$ and $\vec{E}$.

• Option A is correct.
• Option B has the cross product in the reverse order, so the direction is wrong.
• Option C is dimensionally incorrect because it multiplies by $\omega$ instead of dividing by it.
• Option D is incomplete because it does not include division by $\omega$.

Therefore, the correct option is A.