Engineering Electrodynamics

3 Transfer and Conversion of Field Power

3.1 Poynting’s Theorem: Poynting Vector^*

The basis for investigating energy motion in electromagnetic fields is Poynting’s theorem [3.3] and the Poynting vector (Turowski [1.15], [3.4]). Poynting’s theorem says that:

The electromagnetic power P_s flowing into (or flowing out of) a closed volume, across an enclosing surface A, equals to the surface integral of the normal component of the Poynting vector S_n over the entire enclosed surface A:

$P_{s} = \underset{A}{∯} S \cdot d A = \underset{A}{∯} S_{n} d A (3.1)$

where

$S = E \times H (3.2)$

is the Poynting vector, which determines the power and direction of the electromagnetic power flux passing through a surface unit perpendicular to the energy flow direction. Of course,

$S_{n} = E_{t} \times H_{t} (3.2a)$