Antenna Theory Poynting Vector - Antenna Theory

What is Antenna Theory Poynting Vector?

Antennas emit Electromagnetic energy to transfer or to accept information. As a result, the terms Energy and Power are linked with these electromagnetic waves and we have to debate them. An electromagnetic wave has both electric and magnetic fields.

Think through the wave at any direct, which can be watched in both the vectors. The resulting figure displays the illustration of electric and magnetic field components in an Electromagnetic wave.

The electric wave is exist vertical to the propagation of EM wave, however the magnetic wave is horizontally located. Both the fields are at right angles to each other.

Poynting Vector

Poynting vector defines the energy of the EM Wave per unit time per unit area at any given instant of time. John Henry Poynting first resulting this vector in 1884 and hence it was named after him.

Definition − “Poynting vector gives the rate of energy transfer per unit area”

or

“The energy that a wave carries per unit time per unit area is given by the Poynting vector.”

Poynting vector is represented by Ŝ.

Units

The SI unit of Poynting vector is W/m2.

Mathematical Expression

The amount that is used to define the power related with the electromagnetic waves is the instantaneous Poynting vector, which is defined as
$\stackrel{^}{S}=\stackrel{^}{E}×\stackrel{^}{H}$ Where

• $\stackrel{^}{S}$is the instantaneous Poynting vector (W/m2).
• $\stackrel{^}{E}$ is the instantaneous electric field intensity (V/m).
• $\stackrel{^}{H}$ is the instantaneous magnetic field intensity (A/m).

The significant point to be renowned here is that the magnitude of E is greater than H within an EM wave. On the other hand, both of them donate the same quantity of energy. Ŝ is the vector, which has both direction and magnitude. The direction of Ŝ is same as the velocity of the wave. Its magnitude depends upon the E and H.

Derivation of Poynting Vector

To have a perfect idea on Poynting vector, let us go over the derivation of this Poynting vector, in a step-by-step process.
Let us see that an EM Wave, passes an area (A) perpendicular to the X-axis along which the wave travels. While passing through A, in infinitesimal time (dt), the wave travels a distance (dx).

$dx=C\text{}dt$ Where
$C=velocity\text{}of\text{}light=3×{10}^{8}m/s$ $volume,dv=Adx=AC\text{}dt$ $d\mu =\mu \text{}dv=\left({ϵ}_{0}{E}^{2}\right)\left(AC\text{}dt\right)$ $={ϵ}_{0}AC\text{}{E}^{2}\text{}dt$ Therefore, Energy transferred in time (dt) per area (A) is –
$S=\frac{Energy}{Time×Area}=\frac{dW}{dt\text{}A}=\frac{{ϵ}_{0}AC{E}^{2}\text{}dt}{dt\text{}A}={ϵ}_{0}C\phantom{\rule{mediummathspace}{0ex}}{E}^{2}$ Since
$\frac{E}{H}=\sqrt{\frac{{\mu }_{0}}{{ϵ}_{0}}}\text{}then\text{}S=\frac{C{B}^{2}}{{\mu }_{0}}$ Since
$C=\frac{E}{H}\text{}then\text{}S=\frac{EB}{{\mu }_{0}}$ $=\stackrel{^}{S}=\frac{1}{{\mu }_{0}}\left(\stackrel{^}{E}\stackrel{^}{H}\right)$ Ŝ means the Poynting vector.
The above equation offers us the energy per unit time, per unit area at any given instant of time, which is called as Poynting vector.