Why does induction in a loop depend on the contained flux?

[Xilor]

Hiya,

I'm struggling to find/figure out some kind of intuitive explanation why it is the changing flux of the contained area that matters for Faraday's law of induction. It appears odd to me that it is the change of flux through the contained area that matters, rather than the flux that goes through the loop/wire itself. Why would the electrons in the loop be affected when more/less flux passes straight through the middle of the loop, possibly in a region that doesn't even touch the wire?
Would something like a galaxy sized loop still display this behavior? That sounds bizarre

Does anyone have a good explanation? Thanks!

 

[BvU]

Bizarre indeed, isn't it? A question like yours has inspired A Einstein to come up with his "Zur Elektrodynamik bewegter Koerper" . Goes to show great minds think alike .

Read what Feynman and Albert himself have to say about this.

The two phenotypes are https://www.boundless.com/physics/textbooks/boundless-physics-textbook/induction-ac-circuits-and-electrical-technologies-22/magnetic-flux-induction-and-faraday-s-law-161/changing-magnetic-flux-produces-an-electric-field-572-6061/: the integral and differential form of the Maxwell-Faraday equation.

Worth studying: geniuses at work.

 

[Xilor]

Thanks for the links! Glad to hear it isn't a case of missing something very basic haha

So, looking at your links (the boundless.com one specifically), it seems the differential form doesn't include the area anymore, is that correct? That makes it sound to me like that means the flux of the area inside isn't 'actually' relevant, it's just that the area term appears if you transform the differential form further. Is that a correct interpretation? Or am I getting even further off the track?

 

[BvU]

Still on track. Link between the diff and int form is Stokes' theorem. Just math . Easier for the Gauss law Maxwell equation than for the Faraday one ( at least for me it requires some more googling -- or a textbook).

 

[Diegor]

Thanks for the links! Glad to hear it isn't a case of missing something very basic haha

So, looking at your links (the boundless.com one specifically), it seems the differential form doesn't include the area anymore, is that correct? That makes it sound to me like that means the flux of the area inside isn't 'actually' relevant, it's just that the area term appears if you transform the differential form further. Is that a correct interpretation? Or am I getting even further off the track?

It is a very interesting question. Think emf and flux are integrals of the fields. Magnetic field inside the loop, and electric field around the loop. So in this law while you integrate information of the field is lost but it helps to solve problems that have some symetry. As you said in Maxwell equation there is no need to involve area. Is my way to think of it hope it helps.

 

[Xilor]

Still on track. Link between the diff and int form is Stokes' theorem. Just math . Easier for the Gauss law Maxwell equation than for the Faraday one ( at least for me it requires some more googling -- or a textbook).

So to continue the track, since the change of flux is still relevant in the differential form, we are then actually talking about the change of flux that happens in the wire? Or does the change still 'count' the changed flux in the area in between?
Hmm, actually I suppose it would still have to account for the area in between, otherwise you could easily get an inconsistent result with the area based function. If you have some closed loop, and bend the left side rightwards, then the area decreases so the flux decreases, but if you bend the right side rightwards, the area increases and so would the flux, so the current would flow in opposite directions. But from the perspective of the local wire, you're moving it rightwards in both cases, so there shouldn't be a good reason for them to have the current flowing in opposite directions, since the local wire obviously doesn't know anything about the location of the rest of the wire.

It is a very interesting question. Think emf and flux are integrals of the fields. Magnetic field inside the loop, and electric field around the loop. So in this law while you integrate information of the field is lost but it helps to solve problems that have some symetry. As you said in Maxwell equation there is no need to involve area. Is my way to think of it hope it helps.

Hmm, so how is this possible? That some of the information (the area) appears to play a role in one function, yet when it is 'lost' in the differential function results still work out perfectly, even though it actually appears to still be necessary (see the example above).

 

[BvU]

If you have some closed loop, and bend the left side rightwards

That one is easiest to grasp when you look at the Lorentz force: emf is induced in the same direction in the section that moves, whether left or right. But the effect is opposite (cw or acw).

 

[Xilor]

Ah of course, I can't believe I missed that. Alright thanks! That clears that up