Poynting vector which is in the direction of travel of electromagnetic wave is along the vector of E × B


$$Hope you understood$$

Introduction:
The Poynting vector is a mathematical quantity used in physics to describe the energy flow associated with an electromagnetic wave. It is named after the English physicist John Henry Poynting, who first derived it in 1884. The Poynting vector is defined as the cross product of the electric field (E) and the magnetic field (B) vectors.

Poynting Vector Formula:
The formula for the Poynting vector (S) is given as:

S = E × B

where × represents the cross product.

Explanation:
The Poynting vector represents the direction and magnitude of the energy flow in an electromagnetic wave. It describes the rate at which energy is transferred through a unit area perpendicular to the direction of propagation of the wave.

Direction:
The direction of the Poynting vector is perpendicular to both the electric and magnetic fields. It follows the right-hand rule, which states that if the fingers of your right hand are curled in the direction of the electric field, and then bent towards the magnetic field, the thumb will point in the direction of the Poynting vector.

Magnitude:
The magnitude of the Poynting vector is given by the product of the magnitudes of the electric and magnetic fields, multiplied by the sine of the angle between them.

S = |E| |B| sinθ

where |E| represents the magnitude of the electric field, |B| represents the magnitude of the magnetic field, and θ represents the angle between the two fields.

Energy Flow:
The Poynting vector represents the energy flow per unit area perpendicular to the direction of wave propagation. It has units of watts per square meter (W/m^2), which is a measure of power density.

Conclusion:
In conclusion, the Poynting vector is a mathematical quantity that describes the energy flow associated with an electromagnetic wave. It is given by the cross product of the electric and magnetic fields and represents the direction and magnitude of the energy flow. The Poynting vector is an important concept in electromagnetism and is used to understand the transfer of energy in electromagnetic waves.