Can The Faraday Paradox Be Solved?

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I should note that Faraday's disk itself is an exception to Faraday's law. When the disc rotates there is an emf from v×B, but with no change in the linked flux.There are a few others as well, like when two metal plates with slightly curved edges are rocked in a uniform magnetic field, there can be a large change in the flux linkage without the generation of an emf. Also, another interesting point. Notice how when I moved the whole contraption with the multimeter and the red wire on the magnet, there was no induced voltage. That is because everything is moving, even the measurement reference frame. If I only moved the red wire and the magnet together but left the other wires on the table then I would still get a voltage. That means that when I set the magnet on the moving disk, if the measurement device were rotating with the disk then there would be no voltage induced. Here is a great paper that actually tests out spinning the closing circuit. www.nature.com/articles/s41598-022-21155-x. And a lot of people are getting upset about magnetic field lines in the comments. I didn't make up the concept of magnetic field lines, nor Faraday's paradox. This concept and Faraday's paradox have been discussed for over 200 years, lol.

I think the description that magnetic field lines is just a construct make the most sense to me. An electromagnetic field is literally just described with the polarity and strength of a section of the field, and any "lines" just outline areas where the strength is the same, kind of like a pressure or temperature map.

Spinning the magnet and the disc together still produces a voltage because OTHER parts of the circuit are stationary. There is still relative motion between the magnet and the circuit, just not between the magnet and the disc specifically. If you put the entire apparatus on a turntable, then you will get no voltage, as expected. As for why the spinning magnet doesn't produce a voltage, actually it does -- but it produces the SAME voltage on both sides of the circuit. If you connected two multimeters to the circuit, one on each side, with a ground connection in the middle, you would see identical voltage readouts on both multimeters.

Here's the next experiment you need to do: The same spinning disk but your closing wires run parallel to the magnetic field (i.e. Straight up and down), so they don't cut through the field lines.

Your disc magnet has north / south poles on it's faces, and the field lines are concentrated around the edge by the steel cup it's mounted in. When the aluminum disc is rotating under it. it's cutting through the field as it passes by the edge of the magnet. When the magnet is rotating, the edge field is equal all around, so it's not cutting through the conductor, and not generating voltage. If you had a magnet disc with north and south poles alternating around one face, it would work.

Only 60 seconds in and already understand how generators/motors work. 🎉 Phenomenal

The shot you use that shows the scientists talking about something was very helpful to illustrate the concept of scientists discussing science.

I tried this in college with two toroidal magnets out of speakers (same as you had with your drill) but I machined a brass disk mounted to a brass axle such that the two toroidal magnets were placed on either side of the disk and because the disk was only about an eighth of an inch thick, the natural magnetic attraction of the two magnets clamped and rotated with the disk. I then put a multimeter from a brush on the outside edge of the disk and the axle and noted that in either case (whether magnet was held stationary or allowed to spin with the disk) a voltage was developed. I asked my physics professor and we never figured out what was going on. He referenced a very old book where the author claimed that the resolution lie in something to do with relativity (not around during Faraday). But I honestly never understood it sufficiently. I do remember the author claiming that if two equally charged particles a distance x apart were stationary then the force of repulsion was purely electrostatic. But if you as the observer were moving relative to the two particles, then the observed force between them was then a combination of electrostatic and magnetic because the motion gave rise to magnetic field around the charged particles. I found your description excellent. Now subscribed.

I think "cutting field lines" is a red herring. What induces a voltage is a change in flux through a closed circuit, whether the magnet producing that flux is rotating or not is irrelevant. Consider a single wire rotating from the axis. As it rotates past the brushes the enclosed area changes, and flux being field * area this results in the induced voltage. But this requires a finite width brush. In the limit of infinite wires and an infinitely thin brush you will still get a voltage but generate no current. To generate current you require a finite width brush.

The plane of rotation is orthogonal to the field. When the metal is rotating, it is moving at right angles to the field, whether the magnet rotates of not.

REALLY Really need more such videos, As a high school student, it's fascinating for me because I Have learnt about these topics in school and now I'm applying these concepts in this paradoxes which is very cool

Despite my other comment your channel is one of the best on Internet about Physics AND you gave motor and generator brushes a new literal meaning using real brushes.

It sounds really suspicious when the youtuber paid to promote a product says “it has been found that the optimal health benefits are found at 3x the government reccomendations”

there's no paradox (as readily described in the first sentence of the wikipedia article even), your model of allegedly actually existing fieldlines is simply "too coarse". in the case of the spinning disk, you're spinning the electrons rapidly through a magnetic field, while in the case of the spinning magnet you're spinning a magnet that still produces a uniform field. so in the first case the individual electrons experience a locally changing magnetic field, by being physically pushed into/out of it and into/out of the wires/brushes. which also therefore explains your 3rd case of "both moving together": think van-der-graaf generator but made out of "electrons stuck in magnetic field" instead of "stuck as charge on insulating surface". because if the electrons wanted to avoid going along your "loop" bit of the plate, they'd have to move relative to the magnetic field, which as we know requires additional energy. so the lower energy solution is to simply flow through your circuit. there's no such thing as a "moving field", there's just a "moving area in the universal field of magnetic force that we currently claim kinda belongs to this magnet somehow". there's only change in magnetic flux (and of course electric potentials, like that nice low-resistance path through your brushes) to the individual electron. and your "one other point" is plainly wrong, if you spin a bar magnet you very much induce a current, that's literally the whole point of eddys.

This blew my mind. I reasoned out that the full circuit mattered just about before you started explaining it. I wonder what sort of fun could one have with spinning semiconductors. A spinning silicon disk that's npn or pnp could act like a transistor that's spinning constantly. So the magnetic field is like a potential voltage when the base of the disk transistor has a voltage applied to it. I could picture a wild rube goldberg type analog/digital computer. Maybe you get to dope the different layers in 2 dimensions now to create interesting oscillations... a NPN transistor could be swapped to a PNP one, or the values changed so that radially the transistor has different values depending on its rotation. Interesting ideas just from your video.. I love it. Thank you for sharing!

And the movement of the wire across the magnet producing a charge is exactly how an electric guitar pickup works. When you pluck a metal string it moves back and forth over a copper-wound magnet which is grounded to the strings. The tiny electric charge is then amplified; the speed of the back and forth motion of the string electrically reproducing the pitch of the vibrating string.

It's neat that the part where you move a wire over the magnet to create charge is basically how electric guitar pickups work. Never thought of it at a larger scale for some reason.

The science guy was holding the ipad upside down at 8mins 22secs! When magnet and wire are spinning together does the rotating magnet not induce a current across the brushes, negating the effect of the wire? And when one is stationary, the wire will disrupt the magnetic field thereby disturbing flow across the brushes because the wire becomes a second magnet. Just a thought! Thanks for the vid - very interesting!

The way i think of this is regarding the fact that this specific magnet has a rotating symmetry, if you rotate it, the magnetic field wouldn't change. The voltage is generated by a relative motion between the field and the wire, not the magnet itself and the wire. Its not that the magnetic field is stationary, its that rotating it doesnt change it. To change the magnetic field you need to either translate it relative to the wire disc, or rotate it into a non symetric axis. I think this confusion is made because of how people usualy describe the magnetic field visually, with single lines going from the center around the object, giving the impression that rotating the object also rotate those "lines", but the fact is that the magnetic field is homogenous around an specific radius distance ring, it doesnt have any "lines", nor any phisical phenomena that "rotates" with it, because magnetic field is an interaction force, and not a physical object