Pointing Theorem and Explains its Various Terms

The unit of E is volt/m and that of H is A/m, therefore the product of their magnitudes have the unit of power density. The flow of power due to electromagnetic field in a particular direction is of prime importance, the vector product of E and H is used to determine the power of an electromagnetic wave.

If we define the power density vector as:

P=E×H Watt/m².

Using the Maxwell’s equations we have

Equation (1) is known as the point form of pointing theorem. Integrating both sides of (1) over some volume v and applying the divergence theorem, we obtain the integral form of pointing theorem as follows:

The term on the side of (2) is the net inward flux of P into the volume v. The First term on the right side of (2) is a power dissipation term in that it represents the rate of expenditure of energy by the electric field. The second term on the right side of (2) is given by

And represents the time rate of increase of energy stored in the magnetic and electric fields respectively in the volume v.

Therefore (2) states that the net inward flux of the pointing vector through some closed surface is the sum of the power dissipated in the volume enclosed by the surface and the rate of change of energy stored in the volume enclosed by the surface.