What causes EMF induced in Faradays law when only B changes

[Ozgen Eren]

I am having trouble with deducing the origin of Maxwell's Laws, especially Faraday's Law. Obviously some of the laws has to be originated by experiments and the rest should be mere deductions.

I would guess that Lorentz force law is the empirical information where we just named some terms as magnetic field following the experiments. There actually we can also deduce the EMF induced for a moving coil using Lorentz force. Then we get Faraday's law for non-changing magnetic field.

However how do we know that EMF will be induced if we vary B but have stationary coil? For example if I have a line of current and a coil nearby, EMF will be induced if I change the current even if I don't move the coil. Why is that? How do we support this apart from experiment? Can we derive it from Lorentz force law or did we just observed it?

(Saying "EMF is induced because flux changed over time" is not really an answer because it obviously is subject to the same question, why would the change in flux would lead to EMF. How did we know this)

 

[vanhees71]

You can say that the local (differential) Maxwell equations are the collected wisdom about the electromagnetic field in condensed form. You can motivate them from group theory and symmetries of relativistic spacetime but not really derive without empirical input.

 

[Ozgen Eren]

I see, then we could not have Maxwell's law without Faraday's Induction Experiment right? It all boils down to this discovery along with discovery of Lorentz force.

 

[Dale]

Obviously some of the laws has to be originated by experiments and the rest should be mere deductions

None of Maxwells laws can be derived from the others to my knowledge.

They can all be derived from other starting points, like gauge symmetry, charge and flux conservation, etc.

 

[Ozgen Eren]

They can all be derived from other starting points, like gauge symmetry, charge and flux conservation, etc.

Can you suggest an example for Faradays Induction Law? Are we able to define it with using only common sense starting points such as charge and mass conservation
(but not gauge symmetry nor flux conservation as they are more abstract ones. I mean I cannot ask why flux conservation took place but not conservation of *some other abstract mathematical quantity* did not take place. It feels like that would lead a loop that way)

In short, I'm just curious if we have any better explanation than: "Faraday's Induction Law is just the way it is, we noticed it and we are making use of it by deriving other relations by it"

 

[Dale]

Usually you cannot tease them out that finely. You make some assumptions and you get all of Maxwells equations, or half of them. I don't know of any which derive just a single equation.

Here is the one that I mentioned which assumes charge conservation and flux conservation.

http://arxiv.org/abs/physics/0005084

 

[Ozgen Eren]

Thanks for clearing that up. One last follow up question:
If experiments shown Faraday's induction law to be formulated differently, say some weird physics law like "increase in current has a cubic effect, increasing Area reduces induced EMF etc", we would still do the exact same thing then, right? We would just assume conservation of an invented quantity instead of flux, and show that experiments are consistent with conservation of that quantity, therefore it(flux like quantity) may be assumed to exist although it cannot be perceived by itself in any way.

(That is of course when its possible to have conservation law by that weird physics law, I am not sure if is possible with nonlinear relations.)

 

[Dale]

We would just assume conservation of an invented quantity instead of flux, and show that experiments are consistent with conservation of that quantity

Yes. With the caveat that I don't know if the specific results you mention could be made consistent with a Lagrangian of any form. Assuming that it could then, yes, any symmetry of that Lagrangian would be a conserved quantity.