Question

If \( \vec{E} \) and \( \vec{B} \) are the electric and magnetic field vectors of an electromagnetic wave, then the direction of propagation of the electromagnetic wave is

• A. along the direction of \( \vec{E} \)
• B. along the direction of \( \vec{B} \)
• C. parallel to the direction of \( \vec{E} \times \vec{B} \)
• D. perpendicular to the direction of \( \vec{E} \times \vec{B} \)

Hint:

Remember the fundamental relationship between the electric field \( \vec{E} \), magnetic field \( \vec{B} \), and the direction of propagation of an electromagnetic wave. These three vectors form a mutually perpendicular triad, with the direction of propagation given by the direction of \( \vec{E} \times \vec{B} \) (right-hand rule).

Answer 1

The Correct Option is C

In an electromagnetic wave, the electric field vector \( \vec{E} \) and the magnetic field vector \( \vec{B} \) are mutually perpendicular to each other and are both perpendicular to the direction of propagation of the wave.
The direction of propagation of the electromagnetic wave is given by the direction of the Poynting vector \( \vec{S} \), which represents the energy flux density (power per unit area) of the electromagnetic field.
The Poynting vector \( \vec{S} \) is defined as: $$ \vec{S} = \frac{1}{\mu_0} (\vec{E} \times \vec{B}) $$ where \( \mu_0 \) is the permeability of free space.
The direction of the Poynting vector \( \vec{S} \) is the same as the direction of the cross product \( \vec{E} \times \vec{B} \).
The cross product of two vectors results in a vector that is perpendicular to both original vectors, and its direction is given by the right-hand rule.
In the case of an electromagnetic wave, if \( \vec{E} \) and \( \vec{B} \) are perpendicular, their cross product \( \vec{E} \times \vec{B} \) points in the direction of the wave's propagation.
Therefore, the direction of propagation of the electromagnetic wave is parallel to the direction of \( \vec{E} \times \vec{B} \).