Maxwell equations, curl problem

[marcius]

I have a question here about Maxwell's equations: according to faraday's law at some point in space changing magnetic field
with time creates the curl of electric field at that point and according
to Ampere's law with Maxwell's correction changing with time electric
field or electric current density creates the rotor of magnetic field.
So those created fields are circular, so it means that they should have no
beginning, so if electric field vector changing with time at some point
created circular magnetic field at that point, this magnetic field (that
was created) should be zero (or infinity, I'm not sure, but the field is
not defined) at origin point and exist only around it. The same is if
magnetic field induces electric. So if the created circular field is zero
at origin point and exists only aroud that point, it means that both
electric and magnetic field don't exist at the same point at the same
time. So how is with electrmagnetic waves when one field creates another
and they both exist at the same point in space, the graphs of functions (
Eosin(wt+kx) and Bosin(wt+kx) ) show that, because they exist at every
point ?

 

[Antiphon]

Your question seems to say that the curl of a vector field is always zero or infinity. Please explain why.

 

[marcius]

Not like that. the curl is always defined and is neither zero nor infinity. But the field vector is zero, because field is circular, and the field vector is at origin of that circulation, so it should always be zero (or infinity) at its origin point. like there is no magnetic field (or its value its infinity) at the point in space, where the wire is.

 

[pabloenigma]

Not that I really understand your question completely,but,first things first,I would like to point out that : "The Curl Of E is something,this doesn't signify that E has no beginning or end" If E were the Curl of something(E=Curl C,suppose),then you could say E doesn't have a beginning or end.
Baiscally, a field has to be divergenceless if it is without a source.
And Secondly,if a field is divergenceless,ie if it has no beginning or end,then this has no relation to the field being not defined at the origin.The magnetic field of a wire is a special case,a sort of idealization involving a line current.If you considered the wire to be of radius a,then the magnetic field wouldn't blow up at the axis.There are many easily imaginable current distributions such that the Magnetic field doesn't blow up at origin

 

[sardar]

Thank you for your question. The concept of the curl of a vector field is an important one in electromagnetism, and it plays a central role in Maxwell's equations. From your description, it seems that you are referring to the "curl problem," which is a fundamental issue in classical electromagnetism. I will do my best to explain this concept and address your question.

Maxwell's equations are a set of four equations that describe the behavior of electric and magnetic fields in space. They were first formulated by James Clerk Maxwell in the 1860s and have since been refined and extended by other scientists. These equations are fundamental to our understanding of electromagnetism and have been used to make many important predictions and discoveries.

One of the equations, Ampere's law with Maxwell's correction, describes the relationship between changing electric fields and magnetic fields. It states that a changing electric field creates a magnetic field, and vice versa. This is known as electromagnetic induction. Faraday's law, on the other hand, describes how a changing magnetic field creates an electric field.

Now, to address your question about the curl problem: The curl of a vector field at a particular point in space is a measure of how much the vector field is rotating or swirling around that point. In the case of electromagnetic fields, the curl represents the circular motion of the fields around each other. This circular motion is what allows electromagnetic waves to propagate through space.

It is important to note that the curl is a mathematical concept and does not necessarily have a physical interpretation. In other words, it is a way for us to describe the behavior of the fields, but it does not necessarily mean that the fields themselves are circular.

To answer your question about the existence of both electric and magnetic fields at the same point in space, it is important to understand that the equations you mentioned, Eosin(wt+kx) and Bosin(wt+kx), are mathematical representations of the electric and magnetic fields, respectively. These equations show that the fields exist at every point in space, but they do not necessarily have to be zero at the same point at the same time. In fact, the fields can have different values at the same point, as long as they satisfy Maxwell's equations.

In summary, the curl problem is a mathematical issue that arises when trying to describe the behavior of electromagnetic fields. It does not mean that the fields themselves are circular, but rather that they have a circular relationship with each other. The