Rate of energy flow
The Poynting vector, named after John Henry Poynting, is a mathematical quantity used in physics to describe the rate at which energy is flowing in an electromagnetic field. It is denoted by the symbol S.

Definition
The Poynting vector is defined as the cross product of the electric field vector E and the magnetic field vector B. Mathematically, it can be represented as:

S = E x B

Here, "x" represents the cross product operation. The resulting vector S represents the flow of energy per unit area per unit time.

Units
The units of the Poynting vector are watts per square meter (W/m^2) in the International System of Units (SI).

Physical interpretation
The Poynting vector gives us information about the direction and magnitude of the energy flow in an electromagnetic field. Its direction is perpendicular to both the electric and magnetic field vectors, following the right-hand rule. The magnitude of the vector represents the amount of energy flowing per unit area per unit time.

Energy flow in electromagnetic waves
In the case of electromagnetic waves, such as light, the Poynting vector tells us the direction and rate at which energy is being transported. The energy is carried by the electric and magnetic fields, which oscillate perpendicular to each other and to the direction of wave propagation.

Applications
The Poynting vector is an essential tool in analyzing and understanding the behavior of electromagnetic fields. It helps in determining the power flow in transmission lines, calculating the radiation pattern of antennas, and studying the interaction between electromagnetic waves and matter.

In conclusion, the Poynting vector provides information about the rate of energy flow in an electromagnetic field. It is calculated as the cross product of the electric and magnetic field vectors and represents the energy flow per unit area per unit time.