# Poynting theorem

Introduction:-

Poynting theorem is used to get an expression for propagation of energy in a medium.

It gives the relation between energy stored in a time-varying magnetic field and the energy stored in time-varying electric field and the instantaneous power flow out of a given region.

EM waves propagates through space from source to destination. In order to find out power in a uniform plane wave it is necessary to develop a power theorem for the EM field known as poynting theorem.

The direction of power flow is perpendicular to and in the direction of plane containing and .

i.e, it gives the direction of propagation .

Watts/m2  (or)   VA/m2.

Proof:-

from Maxwell’s  equations

the above equation has units of the form current density Amp/m2. When it gets multiplied by V/m. The total units  will  have of the form power per unit volume.

Amp/m2 Volts/m.

Amp. Volt/m3 Watts/m3 Power/volume.

by using the vector identity

then

.

from the equation of Maxwell’s

by using the vector identity

if

from EQN(I)   ,

by integrating the above equation by over  a volume

by converting the volume integral to surface integral

.

the above equation gives the statement of Poynting theorem.

Poynting theorem:-

It states that the net power flowing out of a given volume is equal to the time rate of decrease in the energy stored with in that volume V and the ohmic losses.