Proof of Poynting Theorem
Statement: At any point in a uniform plane wave, the cross product of electric field E and magnetic field H gives a measure of the rate of energy flow per unit area at that point.
using the Maxwell equation We can Write as:
-(1)
-(2)
taking a dot product with E
-(3)
using identity, we can Write
or
put the value of Equation 3
-(4)
-(5)
From Equation 2, take dot product with H
….where = permeability
put the value in Equation 5
-(6) Where
Lets us consider the term
Similarly, we can Write as
put these values in Equation 6
Taking volume integral
(rate of energy flow) and = power loss, =rate of decrease in electromagnetic wave energy.
Hence, poynting theorem is proved
In a uniform plane wave, the first term and next term combine, then something energy loss occurs. These energy rates per unit area are called the poynting vector.
Note: Take all Taking All quantity in the vector form.
Poynting Theorem
The Poynting Theorem which was named After the British Physicist John Henry Poynting is a concept in electromagnetism that describes the energy inflow in an electromagnetic field. It Establishes a connection between the electromagnetic fields and the rate of energy transfer in a given region of space. Mathematically, it’s expressed as the cross-product of the electric field( E) and the magnetic field( H). It represents the power per unit area, or intensity, of the electromagnetic field. In this article, we will be Going Through The Poynting Theorem and its Mathematical Representations and Derive Some Equations.
Table of Content
- What is the Poynting Theorem?
- Mathematical Representation
- Proof of Poynting Theorem
- Derivation of Average power
- Derivation of Average Power Density
- Advantages and Disadvantages
- Application
- Solve Example
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