If we define the power density vector as:
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.