Poynting theorem & Poynting vector

The Poynting theorem represents the time rate change of electromagnetic energy within a certain volume plus the time rate of energy flowing out through the boundary surface is equal to the power transferred into the electromagnetic field.
This statement follows the conservation of energy in electromagnetism and is known as the Poynting theorem.

1. Poynting Theorem & Poynting Vector Mr. VIKRAM SINGH Assistant Professor Department of Applied Sciences & Humanities (Physics) Institute of Technology & Management (ITM) Meerut (IAMR Group Of Institutions, Gaziyabad )

2. Poynting Theorem We know that ……1 ……….2 ………..3 …………4 Now multiplying eq.3 by ‘H’ & eq.4 by ‘E’ H ……….5 E …6  

3. Poynting Theorem Now subtracting eq. 6 from eq.5 ……..7 Integrating over a volume ‘V’ bounded by surface ‘S’ ……8 Now with the help of Gauss divergence theorem change volume integrating into surface integration  

4. Poynting Theorem Where J- Current Density, E- Electric Field Vector ,D- Displacement Charge vector & H - Magnetic field Vector The term is said to be Poynting vector.  

5. Interpretation of   The term represent the amount of energy crossing the closed surface per second. The vector is called Poynting vector & representing by the symbol S. S= This term also represent the energy flow per unit time per unit area. Therefore the Physical interpretation of Poynting vector indicates power flux.  

6. Interpretation of   The electromagnetic force due to field vector E & B acting on the charged particles is Here the magnetic force always be perpendicular to velocity and so magnetic field does no work. The rate of doing work by the electromagnetic field E & B is If is the mechanical force, the work done against electromagnetic field vector is  

7. If electromagnetic field consists of group of charges then Here Current density is given by Therefore the term represent, the rate of energy transferred into the electromagnetic field through the motion of free charge in volume ‘V’.   Power density i.e. transferred into EM-field

8. Interpretation of   The electrostatic and magneto-static energy is Electrostatic energy in volume ‘V’ Magneto-static energy in volume ‘V’ Therefore is electromagnetic field energy in volume ‘V’ & so the term represent the rate of electromagnetic energy stored in volume ‘V’.  

9. Interpretation of   This equation represent time rate change of electromagnetic energy within a certain volume plus time rate of energy flowing out through the boundary surface is equal to the power transferred into electromagnetic field. This statement follow conservation of energy in electromagnetism and is known as Poynting theorem.

10. References Staya Prakash; Engineering Physics; Pragati Prakashan . Poynting's theorem; https://en.wikipedia.org/wiki/Poynting%27s_theorem#:~:text=4%20Alternative%20forms-,Definition,energy%20flux%20leaving%20that%20region . Maxwell’s Equations : Poynting Theorem; Lecture 30: Electromagnetic Theory Professor D. K. Ghosh, Physics Department, I.I.T., Bombay. Electromagnetic Theory; Devid J. Griffth . https://youtu.be/aCTRjVEmeC0.

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