Any charges moving for any reason. It is a general proof.Zubair Ahmad said:Which charges is he talking about and why would they move?
Ok the current density J which comes in proceeding steps is due to motion of these charges but when he uses ampere Maxwell law he relates it to same E and B which are due to some other source.Dale said:Any charges moving for any reason. It is a general proof.
Poynting's Theorem, also known as the Poynting Vector Theorem, is a fundamental concept in electromagnetism. It describes the relationship between the electromagnetic fields and the energy flow in a given region of space. It is closely related to Griffiths' Electrodynamics, which is a widely used textbook on the subject.
The mathematical equation for Poynting's Theorem is given by S = (1/μ0)E x B, where S represents the Poynting vector, E is the electric field, B is the magnetic field, and μ0 is the permeability of free space. This equation represents the flow of electromagnetic energy through a given area in space.
Poynting's Theorem has several practical applications, including the study of electromagnetic radiation, the design of antennas and circuits, and the analysis of energy transfer in various devices. It is also used in the development of renewable energy sources such as solar panels, as it describes the flow of energy from the sun to the Earth.
Poynting's Theorem is based on the assumptions of perfect conductors and idealized fields, which may not accurately represent real-world scenarios. Additionally, it does not take into account the effects of quantum mechanics, which are necessary to fully understand the behavior of electromagnetic fields at a subatomic level.
There are some controversies surrounding Poynting's Theorem, particularly in its application to the concept of electromagnetic momentum. Some argue that the theorem does not accurately account for the total momentum of an electromagnetic field, while others claim that it is a valid and useful concept. The debate continues among scientists and researchers in the field of electromagnetism.