EM field and its sources

[fisico30]

EM field and its sources...

hello forum,

a simple question about EM field and its sources.
In a time-varying situation, maxwell equations tell that the E field has the time-changing charge density rho as a source, while the B field has the time-changing current density J.

But both fields are actually and fundamentally generated by charges, static, moving, or accelerating (i.e. rho).
Why is the source distinction useful? After all, the continuity eqn link rho and J.

On the other hand, in antenna theory, the E field (and the B) is generated by the time-varying current source in the antenna. There is no need to talk about the charge density rho... J is fine and enough.

Why in electrodynamics we just don't use J?
thanks!

 

[eljose79]

Dear fellow scientist,

Thank you for your question about the sources of the electromagnetic (EM) field. This is a common area of confusion, so I am happy to clarify it for you.

Firstly, it is important to understand that the sources of the EM field are not limited to just charges. While charges are indeed one source, there are other sources as well, such as time-varying currents and changing magnetic fields. This is why the distinction between the two fields, E and B, is useful. The Maxwell equations take into account all of these sources to accurately describe the behavior of the EM field.

Secondly, the continuity equation does link the charge density and current density, but it does not make them interchangeable. While they are related, they are not the same thing. The charge density represents the amount of charge per unit volume, while the current density represents the amount of current per unit area. In some cases, one may be more useful to consider than the other, but both are important in understanding the behavior of the EM field.

In antenna theory, the focus is on the generation of EM waves, which are created by the time-varying current in the antenna. However, this does not mean that the charge density is not important. In fact, the charge density is still present and plays a role in the behavior and propagation of the EM waves.

In electrodynamics, we use both the charge density and current density because they are both important in fully describing the behavior of the EM field. While in some cases one may be more relevant, it is essential to consider both sources in order to have a complete understanding of the EM field.

I hope this helps to clarify the use of both charge density and current density in describing the sources of the EM field. If you have any further questions, please do not hesitate to ask.

 

[charng]

Thank you for your question about the EM field and its sources. The source distinction between the electric and magnetic fields is important because it helps us understand the underlying physical processes that give rise to these fields. While both fields are ultimately generated by charges, the way they interact with these charges is different, leading to the need for separate sources in Maxwell's equations.

For the electric field, the source is the time-changing charge density rho. This is because the electric field is created by the presence of charges and their interactions with each other. As charges move or change, they create an electric field that can influence other charges in the vicinity. On the other hand, the magnetic field is created by the motion of charges, as represented by the time-changing current density J. This is because the magnetic field is a result of the interactions between moving charges, such as in a wire carrying current.

In antenna theory, the source of the EM field is the time-varying current source in the antenna. This is because the antenna is specifically designed to generate an electromagnetic wave, and the current in the antenna is responsible for creating the EM field. In this case, the charge density rho is not as relevant since it is the motion of charges in the antenna that is creating the field.

In electrodynamics, we use both the charge density rho and the current density J because they are both important in understanding the behavior of the EM field. The continuity equation links these two quantities together, showing the relationship between charge and current in a given system. Using both sources allows us to fully describe the behavior of the EM field in different situations.

I hope this helps to clarify the importance of the source distinction in understanding the EM field. Let me know if you have any further questions. Thank you for your interest in this topic.