Can The Faraday Paradox Be Solved?

this is a magnet it has magnetic field lines that move up from the top and go down through the bottom like this if I take a wire and cut it across those magnetic field lines it actually creates a voltage in The Wire so if I hook up my voltmeter to the end of The Wire then sure enough when I move the wire over the top it creates a voltage but only when I'm moving it if I stop then the voltage drops to zero or I can set the wire on the ground and move the magnet over the top and it creates the same voltage but if I move both the wire and the magnet together then they also don't create any voltage so there has to be relative motion between the magnet and the wire so in order to create this voltage I have to constantly be moving the wire cutting across the magnetic field lines but what if I just replace this location of wire with a section that's always moving like a disc spinning so if this spins I still need a way to connect it to the rest of the circuit so to do that I'm just going to put some some wire brushes on the side then I'm going to stick this brush underneath that'll contact the axle spinning so now my closed circuit goes like this from the multimeter to this brush across the disc down this brush back to the multimeter now for my magnet I'm not going to use that giant magnet I had before that's way too strong but I'm going to use this uniform disc magnet so I can apply a uniform magnetic field over the top of the disc here okay now let's turn it on so there's no voltage but when I move the magnet over the top then I generate a voltage that's because my section of wire right here is continually cutting through the magnetic field what I've created here is called Faraday's disc it's an electric generator that was invented in 1821 by Michael Faraday and it was the first device ever created that could generate electricity using the laws of induction Faraday's exploration of this simple generator laid the groundw work for his later formulation of Faraday's law which quantitatively described the relationship between changing magnetic flux and induced electromotive force or voltage but there was a problem according to Faraday's new law his own device created a paradox that still persist to this day let me show you what the problem is but first I'd like to thank the sponsor for this video drink element element is a zero sugar electrolyte drink mix born from the growing body of research revealing the Optimal Health out outomes occur at sodium levels two to three times government recommendations each stick pack delivers a meaningful dose of electrolytes free of sugar artificial colors or other dodgy ingredients that is good taste it that is really good it's so good element is formulated for anyone on a mission to restore Health through hydration element is even being used by professional athletes it's the exclusive hydration partner for the USA weightlifting team and many other Olympic athletes there are so many flavors to choose from but one of 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that if I spin the magnet above the the disc while the disc is standing still I should also get a voltage so now I put this on the end of the drill and I can spin the magnet like this so let's see what happens now if I spin the magnet over the disc when I spin the magnet I get no voltage generated it's exactly zero so that's not good but it gets worse remember the scenario where I moved the magnet and the wire together it didn't create a voltage so now let's try that with our disc what if I just place the magnet on the disc so they're moving at the exact same relative speed to each other I still generate a voltage if I just set the magnet on top of the spinning disc they're both spinning at the exact same speed so there's no relative motion between the disc and the magnet but when I turn it on I get a voltage so when we expect it to get no voltage it's generating a voltage and we expect no voltage there is a vol voltage what's going on here so the problem is this if both the disc and the magnet aren't spinning no relative motion between them I get no voltage but if I spin the disc and the magnet is standing still on top then I get a voltage but if I spin the magnet on top with the disc standing still then I get no voltage but then if I put the magnet on the disc so that they're both spinning and no relative motion between them then I get a voltage this is known as Faraday's Paradox it goes against our intuition and challenges the very heart of the physics that were first used to describe it so let us see if we can resolve the Paradox and understand why this is happening initially Faraday proposed that when the magnet rotates the magnetic field stays stationary so the disc cutting through the field lines gives rise to an electromotive force or EMF observable as the induced voltage across the disc but he later changed that point of view based on the fact that when you move a magnet linearly the field also moves with it so he thought that the filled lines must rotate with the magnet as well for example if I spin this bar magnet under this magnetic viewing paper we can see the magnetic field rotates with it but if the field rotates with the magnet then the spinning magnet should induce a voltage on a stationary disc so which is it does the field rotate with the magnet or remain stationary well it turns out that whether you view the magnetic field as rotating or remaining stationary the Paradox can be solved when we take the whole circuit into account remember that in in order to measure the voltage we have other wires that I'll call the closing wires because these are the wires required to complete the circuit remember that underneath here we have a small portion of wire touching the axle so there's a small piece of wire underneath here so this piece of wire is cutting the magnetic field lines as well so now with these wires taken into account let's look at the scenario where only the disc is spinning if the magnetic field is stationary or co-rotating we would get the same result since the magnet it's not spinning so the disc cuts the magnetic field lines and a voltage is induced and the closing wire is neutral because it doesn't cut any magnetic field lines cuz it's not spinning meaning it's not moving through any magnetic field lines but now let's look at the scenario where the magnet is spinning and the disc is still in this case if the field is stationary the disc is neutral since it isn't moving through any magnetic field lines so there's no induced voltage but if the field is co-rotating with the magnet then the disc is cutting through the magnetic field lines and there's a current induced but also the closing wire is cutting the magnetic field lines as well and it's polarized the same way so no voltage is induced in the circuit and finally if both the magnet and disc are rotating together and we take the scenario that the field is stationary then it's the same as in the scenario one where just the disc is rotating and the disc cuts the magnetic field lines and if the field is co-rotating then the disc doesn't cut the magnetic field lines but the Clos wire does so there's still a voltage induced which is what we see experimentally so we can see that in either case we can resolve the Paradox whether or not we view the magnetic field as stationary or rotating when we take the whole circuit into account so there really is no Paradox so why did I say that this is still being discussed today well because physicists can't agree if the field is rotating or not you can see that experimentally we expect the same results so we can't can't tell from this experiment whether or not the field actually rotates with the magnet or not and it turns out that almost any experiment that you create you wouldn't be able to tell that the field is rotating or not rotating there are well- reviewed published papers that say it does rotate with the magnet and others that say it doesn't and then others say that the magnetic field lines don't exist at all but they're just used as mathematical tools and not a real entity so it's pointless to discuss whether a field rotates with the magnet or not and then we can just have some fun making the motor version of Faraday's disc by sticking a magnet to a battery and touching it with a wire and thanks for watching another episode of the action lab and we'll see you next time

Channel: The Action Lab

Views: 1,276,233

Keywords: faraday paradox, homopolar generator, michael faraday, the action lab

Id: _cUXNwp2Ock

Length: 9min 20sec (560 seconds)

Published: Thu Feb 29 2024