Question

An electromagnetic wave is propagating in the positive x direction. At a given moment in time, the magnetic field at the origin points in the positive y direction. In what direction does the electric field at the origin point at that same moment?a. Positive xb. Negative xc. Positive yd. Negative ye. Positive zf. Negative z

Answer 1

To solve this exercise it is necessary to take into account the concepts related to the magnetic field and its vector representation through the cross product or vector product.

According to the definition the direction of the electromagnetic wave propagation is given by

$\hat{n} = \vec{E} \times \vec{B}$

Where,

E = Electric Field

B = Magnetic Field

According to the information provided, the direction of propagation of the electromagnetic wave is on the X axis, which for practical purposes we will denote as $\hat {i}$, on the other hand it is also indicated that the magnetic field is in the Y direction, that for practical purposes we will denote it as $\hat {j}$. In this way using the previous equation we would have to,

$\hat{n} = \vec{E} \times \vec{B}$

$\hat{i} = \vec{E} \times \hat{j}$

The cross product identity is

$\hat{i}=-\hat{k} \times \hat{j}$

From the equation we can notice that the electric field would be given by,

$\vec{E} = -\hat{k}$

Therefore the direction of electric field is negative z-axis.