# Maxwell equations, curl problem

1. Jan 29, 2012

### 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 ?

Last edited: Jan 29, 2012
2. Jan 29, 2012

### Antiphon

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

3. Jan 29, 2012

### 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.

4. Jan 29, 2012

### 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 doesnt signify that E has no beginning or end" If E were the Curl of something(E=Curl C,suppose),then you could say E doesnt 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 wouldnt blow up at the axis.There are many easily imaginable current distributions such that the Magnetic field doesn't blow up at origin