Consolidating maxwells equation with relativity

Click For Summary

Discussion Overview

The discussion revolves around the relationship between Maxwell's equations and the principles of relativity, particularly in the context of a thought experiment involving a large conductor loop and a magnet. Participants explore the implications of turning off the magnet and how it relates to induced EMF and magnetic flux, questioning the consistency of these concepts with relativistic effects.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant suggests that turning off a magnet at the center of a large conductor loop should induce an EMF along the loop, raising questions about the implications of relativity on this process.
  • Another participant counters that Maxwell's equations do not predict an induced EMF in this scenario, prompting a discussion about Faraday's Law and the rate of change of magnetic flux.
  • There is a consideration of whether the rate of change of flux is zero in the given thought experiment, with one participant expressing confusion about how turning off the magnet does not reduce the flux through the loop.
  • A later reply introduces the idea that the net magnetic flux can be zero due to the nature of magnetic field lines, suggesting that a change in flux would require field lines to cross the boundary loop at the speed of light.
  • Another participant raises a different scenario involving a current-carrying wire and questions whether turning off the current would instantaneously change the magnetic field integral along the loop.
  • One participant challenges the previous statements by asking for calculations related to the thought experiment, indicating a desire for a more rigorous examination of the claims made.

Areas of Agreement / Disagreement

Participants express differing views on the implications of Maxwell's equations in the context of relativity, with no consensus reached on whether an induced EMF occurs when the magnet is turned off. The discussion remains unresolved as participants explore various aspects of the problem.

Contextual Notes

Participants highlight limitations in understanding the rate of change of magnetic flux and the conditions under which it may change, particularly in relation to the speed of light and the behavior of magnetic field lines.

Fibo112
Messages
149
Reaction score
3
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.
 
Physics news on Phys.org
Fibo112 said:
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.
 
Dale said:
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?
 
Fibo112 said:
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 can't really see why. How does turning off the magnet not reduce its flux through the loop?
 
Fibo112 said:
I guess it must be zero, but I can't 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 what's 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)
 
Fibo112 said:
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?
 
Fibo112, you've written the words "Maxwell's equations", but I notice you haven't written any equations. Have you tried to calculate the result of your thought experiment?
 
  • Like
Likes   Reactions: Cryo and Dale

Similar threads

Undergrad How Does the Maxwell-Faraday Law Apply to Stealth Magnets and EMF Induction?
  • · Replies 27 ·
Replies
27
Views
3K
Undergrad Magnetic field inside a capacitor
  • · Replies 16 ·
Replies
16
Views
2K
Undergrad The vector math of relative motion of wire-loop & bar magnet
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Confusion when dealing with loops and surfaces with Maxwell equations
  • · Replies 2 ·
Replies
2
Views
1K
Graduate An Interesting Question on Faraday's Law of Electromagnetic Induction
  • · Replies 11 ·
Replies
11
Views
3K
Graduate Maxwell's Law of Induction - How Does it Work?
  • · Replies 7 ·
Replies
7
Views
4K
Undergrad Charge movement relative to magnetic field frame dependence/invariance
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Why are Maxwell's equations and the Lorentz force "so different"?
  • · Replies 9 ·
Replies
9
Views
3K
Graduate Relationship between magnetic potential and current density in Maxwell
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Faraday's Law with Zero Resistance Current Loop
  • · Replies 2 ·
Replies
2
Views
7K