Explain why it is necessary to use physical electric and magnetic fieldswhen determining the Poynting vector N

The Poynting vector, denoted by N, is a fundamental concept in electromagnetism that represents the directional energy flux density of an electromagnetic field. It is named after its inventor, John Henry Poynting. The Poynting vector is defined as the cross product of the electric field (E) and the magnetic field (B), i.e., N = E × B.

Here's why it's necessary to use physical electric and magnetic fields when determining the Poynting vector:

1. Physical Representation: The Poynting vector is a physical quantity. It represents the energy flow per unit area per unit time. Therefore, it must be determined using physical quantities, which in this case are the electric and magnetic fields.

2. Mathematical Definition: As mentioned above, the Poynting vector is defined as the cross product of the electric and magnetic fields. This mathematical operation can only be performed with these two physical fields.

3. Energy Transfer: The Poynting vector is used to calculate the power crossing a certain area in the space. This power is due to the electromagnetic field, which is composed of the electric and magnetic fields. Therefore, to calculate this power, we need to know the values of these two fields.

4. Direction of Energy Flow: The direction of the Poynting vector gives the direction of energy flow. This direction is determined by the cross product of the electric and magnetic fields. Therefore, these two fields are necessary to determine the direction of energy flow.

5. Magnitude of Energy Flow: The magnitude of the Poynting vector gives the rate of energy transfer per unit area. This magnitude is determined by the magnitudes of the electric and magnetic fields and the angle between them. Therefore, these two fields are necessary to determine the rate of energy transfer.

In conclusion, the physical electric and magnetic fields are necessary when determining the Poynting vector because they define its direction, magnitude, and physical significance.