Energy is transported through space by means of electromagnetic waves, let the material inside the surface S be isotropic homogeneous and characterised by permeability µ and permittivity ε and conductivity σ

Maxwell’s IIIrd and IVth equations are as follows

Curl E = -dB/dt

Curl H = J + dB/dt

Taking scalar product of both sides of equation (1) and equation (2) respectively with Hand E

H cual E = – H dB/dt

E cual H =E(J+ dB/dt)

Now, subtracting equation (3) from equation (4), we get

(curl H –H curl E ) =E .J +E . dB/dt + H dB/dt

J . dB/dt + H dB/dt

Now, using vector identity

Div (E x H ) =H curl E –E curl E

putting above value in L.H.S. equation (5) may be expressed as

-div (E x H) = J.E+ E . dB/dt + H dB/dt

Now, if the medium is linear so that the relations

Now, integrating this equation over the volume V bounded by the surface S, we get

By applying Gauss transformation formula in L.H.S.

The above equation (10) represents the poynting theorem.

7**.20.1 Physical Significance or Interpretation of terms of Poynting Theorem**

** **

(a) Interpretation of term ʃ _{V}. Ed V: The current distribution represented by the vector J can be considered as made up of various changes qi moving with velocity

where E j denotes the electric field at the position of charge q j According to Lorentz force equation, the force experienced by point charge is given by

f =q (E +v + B)

We know that workdone is equal to force x displacement

Dw =F .dl

= q (E +v x B )dl

= q .E dl +q (v x B) dl

= q E dl +dl (dl/dt x B) q

=q E dl + dl +(dl x dl/dt) .B q

Dw = q E dl + 0

Dw/dt =q E dl/dt

Dw /dt =q E .v

taking all the charges into consideration, we get

Dw /dt =Ʃq_{j}(E_{j} v_{j})

From equations (1) and (2)

This shows that this term represents the rate at which the work is done by the field

on the charges.

**(b) Interpretation of term**

The above equation represents the time rate of increase in energy stored in the electric and magnetic field respectively in volume.

**(c) Interpretation of the term**

Since L.H.S. shows the rate of change of work done or power so this term must shows the power flow into volume V across the surface 5 or the power flow out of volume V across the surface S

where P =Ex H

where P = E x H is known as Poynting vector and hence the meaning of power density associated with electromagnetic field at a point

Dimension of P = [M ^{-3}]

unit of P = Watt/meter2

where P =Ex H

where P = E x H is known as Poynting vector and hence the meaning of power density associated with electromagnetic field at a point

Dimension of P = [M ^{-3}]

unit of P = Watt/meter2