# Consolidating maxwells equation with relativity

Hello
I know that maxwells equations are consistent with relativity. The following thought experiment seems to imply otherwise so I am wondering where my mistake lies.

Lets say we have some very large conductor loop(with a radius of many lightyears). At the center of the loop is some magnet which has a magnetic flux through the loop. Now to me it seems that maxwells equations imply that if I start to "turn off" this magnet, then while I am turning it off there will be an induced EMF along the loop. But how can be? Relativity would imply that the outside of the loop is not effected by what I do in the center for years.

Dale
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2021 Award
Now to me it seems that maxwells equations imply that if I start to "turn off" this magnet, then while I am turning it off there will be an induced EMF along the loop.
Here is where the mistake lies. Maxwell’s equations do not predict this.

Here is where the mistake lies. Maxwell’s equations do not predict this.
Ok. Doesnt Faradays Law say that the EMF around a closed loop is equal to the rate of change of the magnetic flux through that loop?

Dale
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2021 Award
Ok. Doesnt Faradays Law say that the EMF around a closed loop is equal to the rate of change of the magnetic flux through that loop?
Yes. But what is the rate of change of the flux in your example?

I guess it must be zero, but I cant really see why. How does turning off the magnet not reduce its flux through the loop?

Dale
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2021 Award
I guess it must be zero, but I cant really see why. How does turning off the magnet not reduce its flux through the loop?
Consider a magnetic field which is constrained to some finite region and an arbitrary plane crossing that region. Since the field lines form closed loops, any line which crosses the plane in one direction must cross it in the other direction also. The net flux is therefore 0, regardless of the strength of the field.

The only way for the flux to change is for the field lines to cross the boundary loop. This happens at c, not instantaneously.

Ok, I think I understand whats going on. How about the case where there is a current carrying wire going through the center of the loop and the current is suddenly turned off. Wont this instantaneously change the amount of current going through the loop?( and thereby change the magnetic field integral along the loop)

Dale
Mentor
2021 Award
Wont this instantaneously change the amount of current going through the loop?( and thereby change the magnetic field integral along the loop)
Let’s suppose that were correct. What would the instantaneous change in the magnetic field cause?

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