# 6. Electromagnetism (Electromagnetic Waves)

## The problem asks you to determine

• The direction of the magnetic field of a plane electromagnetic wave.

## The problem gives

• The electric field. It is given by $\vec{E} = E_0 (\vec{e}_x + \vec{e}_y) \sin(kz-\omega t)$

• Property of the electromagnetic waves: The oscillations of electric and magnetic fields are perpendicular to each other, and also perpendicular to the direction of energy and wave propagation.
• From the electric field $\vec{E} = E_0 (\vec{e}_x + \vec{e}_y) \mathbf{\sin(kz-\omega} t)$, you should find out that the direction of wave propagation is +z direction.

## Solution

Let’s first consider the fact that two fields are perpendicular to the direction of wave propagation. The possible answers could be (B) and (C).

However, the direction of (C) is parallel to that of the electric field. Thus the choice (C) cannot be an answer.

Therefore, a remaining and the only correct answer is (B).

(B) $- \vec{e}_x + \vec{e}_y$