The Poynting vector is a quantity in electromagnetism that describes the direction and magnitude of electromagnetic energy flow. It is named after John Henry Poynting, who introduced it in 1884.
The Poynting vector (S) is defined as the cross product of the electric field vector (E) and the magnetic field vector (B):
S = E x B
where "x" represents the cross product.
The direction of the Poynting vector gives the direction of energy flow, while its magnitude represents the rate at which energy is being transported per unit area. The units of the Poynting vector are watts per square meter (W/m²).
The Poynting vector is used to find the energy associated with electromagnetic fields. The energy per unit volume (u) carried by the electromagnetic field is given by:
u = (1/2ε₀) * E² + (1/2μ₀) * B²
where ε₀ is the permittivity of free space and μ₀ is the permeability of free space. The Poynting vector can be related to the energy density by:
u = |S|
In other words, the energy density is equal to the magnitude of the Poynting vector.
The Poynting vector is a useful tool in studying the energy transfer in electromagnetic waves. It helps in understanding how energy is propagated and transported through space by electromagnetic fields, such as in the case of radio waves, light, and other forms of electromagnetic radiation.