Maxwell equations, curl problem

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Discussion Overview

The discussion revolves around the implications of Maxwell's equations, particularly focusing on the concepts of curl and the behavior of electric and magnetic fields at specific points in space. Participants explore the nature of fields generated by changing magnetic and electric fields, questioning how these fields can coexist at the same point in space, especially in the context of electromagnetic waves.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions how changing magnetic fields create circular magnetic fields that are zero or undefined at their origin, suggesting a contradiction in the coexistence of electric and magnetic fields at the same point.
  • Another participant challenges the assertion that the curl of a vector field is always zero or infinity, asking for clarification on this point.
  • A different participant argues that while the curl is defined, the field vector may be zero at the origin due to the circular nature of the field, referencing the magnetic field around a wire as an example.
  • Another response emphasizes that the curl of a field does not imply that the field has no beginning or end, and discusses the concept of divergenceless fields in relation to sources.
  • This participant also introduces the idea that considering a wire with a finite radius can prevent the magnetic field from becoming undefined at the origin, suggesting that various current distributions can yield different behaviors of the magnetic field.

Areas of Agreement / Disagreement

Participants express differing views on the implications of curl and the behavior of fields at their origins. There is no consensus on the interpretations of these concepts, and the discussion remains unresolved.

Contextual Notes

Participants reference specific cases such as the magnetic field around a wire and the nature of divergenceless fields, indicating that assumptions about field behavior may depend on the context and definitions used.

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

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