Question

The velocity of electromagnetic wave is parallel to:
(A) \[\overrightarrow B \times \overrightarrow E \]
(B) \[\overrightarrow E \times \overrightarrow B \]
(C) \[\overrightarrow E \]
(D) \[\overrightarrow B \]

Answer 1

Hint: When an electromagnetic wave such as light or x-ray or radio wave travels in a medium they all travel in the form of a transverse wave. Now electromagnetic waves are associated with both magnetic and electric fields which move along with them. These field waves are always perpendicular to the direction of motion of the electromagnetic wave.

Complete answer:
Now we know that the electromagnetic waves always propagate in the direction which is perpendicular to the direction of magnetic and electric field associated with them.
So, the options (C) and (D) can be eliminated directly as this option tends to show that the direction of the electromagnetic wave is parallel to the direction of electric and magnetic field.
We need to recall that the cross product of two vectors gives us a new vector whose direction is perpendicular to the direction of the two-vector present.
So according to the Poynting theorem, we cross magnetic field vectors with electric field vectors in order to get the direction of the propagation of the electromagnetic wave.
So, the correct way to get the direction is by crossing the electric field vector with the magnetic field vector.
\[\overrightarrow E \times \overrightarrow B \]

The correct option is (B).

Note:
Now if we \[\overrightarrow E \times \overrightarrow B \] cross we also get the exact value of the speed of the electromagnetic wave. Now we can also see that there is another option which is option (A) in which there is a cross product of vector but here the magnetic field vector is placed first this will give us the direction perpendicular to both the vectors but in the opposite direction to that of the propagation of wave.