Explanation of Lenz's Law phenomena

If we drop a magnet through a copper pipe (without it touching any of the sides), it would fall slower than it would if there were no pipe.

Having the pipe otherwise accelerate the magnet would be in violation of Lenz's law and conservation of energy. I agree that, if there is any interaction between the copper pipe and the magnet, then it should be to decelerate the magnet.

But, why is there even any interaction between the pipe and magnet in the first place? Why can't there just be zero interaction? This way, the magnet is only affected by gravity, just how it would be if it were just a normal wooden or plastic pipe!

Would zero interaction be a violation of some other kind of laws? Such as, the Lorentz force law, or Biot-Savart, or something else? Would zero interaction violate special relativity? Or, some rules of quantum mechanics?

• According to en.wikipedia.org/wiki/Eddy_current, the cause is ultimately Faraday's law of induction combined with the Lorentz force law, which is effective because a metal has mobile electrons. – Chiral Anomaly Jan 15 at 2:29
• My question is about why there is even any interaction at all in the first place. Faraday's and Lenz's laws merely assume this interaction as a given and just describe it quantitatively. Perhaps the answer to my question lies in deeper quantum mechanics or relativity. – ManRow Jan 15 at 2:32
• Is the question really specific to the magnet-falling-in-a-copper-pipe example, or is it really a question about why the Lorentz force (etc) exists? – Chiral Anomaly Jan 15 at 2:33
• Maxwell's equations (including Faraday's law) and the Lorentz force law are both derivable from a single action principle (which respects special relativity), and Lenz's law is derivable from them. The fact that Maxwell's equations and the Lorentz force law work together to satisfy an action principle could maybe be regarded as a sense in which they sort of require each other; but I don't know if that's what you're looking for. That kind of answer wouldn't be specific to the copper pipe example. – Chiral Anomaly Jan 15 at 2:39
• It's shown in the last equation on page 119 in "Chapter 5: The Relativistic Point Particle," fma.if.usp.br/~amsilva/Livros/Zwiebach/chapter5.pdf, for example. I found this example by searching with the keywords "action for particle in electromagnetic field". – Chiral Anomaly Jan 15 at 3:04

If we drop a magnet through a copper pipe (without it touching any of the sides), it would fall slower than it would if there were no pipe.

The simple answer to this would be because there's a flux of magnetic field lines around the magnet.

So as they say there is an induction in the pipe which makes its upper end to gain the same polarity as the magnets lower end falling towards the coil, that creates a repulsion slowing the magnet down.

That is because of the fact that when flux changes through the pipe, it creates an electric field in the conduction and when charges move along electric field lines work is done on them, whether it involves storing potential energy (negative work) or increasing kinetic energy (positive work).

When net positive work is applied to a charge q1, it gains speed and momentum. The net work on q1 thereby generates a magnetic field whose strength (in units of magnetic flux density (1 tesla = 1 volt-second per square meter)) is proportional to the speed increase of q1. This magnetic field can interact with a neighboring charge q2, passing on this momentum to it, and in return, q1 loses momentum.

The charge q2 can also act on q1 in a similar manner, by which it returns some of the momentum that it received from q1. This back-and-forth component of momentum contributes to magnetic inductance. The closer that q1 and q2 are, the greater the effect. When q2 is inside a conductive medium such as a thick slab made of copper or aluminum, it more readily responds to the force applied to it by q1. The energy of q1 is not instantly consumed as heat generated by the current of q2 but is also stored in two opposing magnetic fields

But, why is there even any interaction between the pipe and magnet in the first place? Why can't there just be zero interaction? This way, the magnet is only affected by gravity, just how it would be if it were just a normal wooden or plastic pipe!

Its simply because there are invisible field lines acting to oppose the motion.

So for example : when you hold two bar magnet's , they repel or attract, right ? But you never asked why can there be no interaction, just like holding a two wood logs does nothing.

But that's ridiculous because magnetic force makes them do so. That's the same thing happening here.

Yes it has interction. Beacuse the top side of the pipe will act as a opposite polarity and repel

It looks like what we call Lenz's Law can actually be explained by the Lorentz force and Biot-Savart Law.

Suppose in the classic example of dropping a magnet down a conducting pipe (not touching the walls), the north pole is facing downwards while the south faces up. The relative motion of the magnet and pipe will induce a Lorentz force on the charges in the pipe, specifically in a horizontal direction that will appear counterclockwise around the pipe when viewed from above. By Biot-Savart, such current will then create its own magnetic field, and (inside the pipe) with an orientation against the field of the falling magnet. Hence, we observe Lenz's law.