Question

The poynting vector for an electromagnetic wave is:
 $ \left( A \right)\vec S = \vec E \times \vec H \\ $
 $ \left( B \right)\vec S = \vec E \times \vec B \\ $
 $ \left( C \right)\vec S = \dfrac{{\left( {\vec E \times \vec H} \right)}}{2} \\ $
 $ \left( D \right)\vec S = \dfrac{{\left( {\vec E \times \vec B} \right)}}{2} \\ $

Answer 1

Hint :In order to solve this question, we are going to first define the pointing vector and then, write its formula. Then, we can simplify the formula into some other form. After that, comparing the formula obtained with the options as given above in the question, the correct option is chosen.
The Poynting vector for an electromagnetic wave is defined as:
 $ \vec S = \vec E \times \vec H $
Where, $ \vec E $ is the electric field vector
 $ \vec H $ Is the magnetic auxiliary field
If we represent the pointing vector in terms of the magnetic field,
 $ \vec S = \dfrac{1}{{{\mu _0}}}\left( {\vec E \times \vec B} \right) $
Where, $ {\mu _0} $ is the vacuum permeability
  $ \vec E $ is the electric field vector
 $ \vec B $ is the magnetic field vector.

Complete Step By Step Answer:
Poynting vector is defined as directional energy flux density which is the energy transfer per unit area per unit time of an electromagnetic field. The SI unit of the Poynting vector is the watt per square metre ( $ W{m^{ - 2}} $ ).
The pointing vector is used throughout electromagnetics in conjunction with Poynting’s theorem, the continuity equation expressing conservation of electromagnetic energy, to calculate the power flow in electric and magnetic fields.
Poynting vector is defined as:
 $ \vec S = \vec E \times \vec H $
If we represent the pointing vector in terms of the magnetic field,
 $ \vec S = \dfrac{1}{{{\mu _0}}}\left( {\vec E \times \vec B} \right) $
Here, the option (A) best matches the formula for the poynting vector, thus option $ \left( A \right)\vec S = \vec E \times \vec H $ is the correct answer.

Note :
In an electromagnetic field, the flow of energy is given by the Poynting vector. For an electromagnetic field, this vector is in the direction of propagation and accounts for radiation pressure. However, in a static electromagnetic field the Poynting vector can of course be non-zero.