Answer:
The Poynting vector is a vector quantity that describes the direction and magnitude of the energy flow in an electromagnetic field. It is defined as:
S = E x H
where:
E is the electric field
H is the magnetic field
For a circularly polarized plane wave, the electric and magnetic fields are given by:
E = E_0 e^{i(kz - \omega t)}
H = H_0 e^{i(kz - \omega t)}
where:
E
0
is the amplitude of the electric field
H
0
is the amplitude of the magnetic field
k is the wavenumber
ω is the angular frequency
t is time
The Poynting vector can be calculated as:
S = E_0 H_0 e^{i(kz - \omega t)} \times e^{i(kz - \omega t)}
Simplifying, we get:
S = E_0 H_0 e^{i(2kz - 2\omega t)}
The magnitude of the Poynting vector is given by:
|S| = E_0 H_0
The Poynting vector is a constant that is independent of time and distance because the electric and magnetic fields are sinusoidal functions of time and space. The amplitude of the electric and magnetic fields are constant, so the magnitude of the Poynting vector is also constant.
Step-by-step explanation: