How Does Magnet Size Affect Lenz's Law in Falling Magnet Experiments?

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Discussion Overview

The discussion revolves around the effects of magnet size on Lenz's Law as observed in experiments involving a falling magnet through a tube. Participants explore theoretical implications, practical observations, and the relationship between magnet size and induced electromagnetic effects.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant questions whether a significantly smaller magnet would produce different effects compared to a magnet that is roughly the same size as the tube.
  • Another participant suggests that the proximity of the magnet to the metal tube is crucial for effectively cutting the magnetic flux, implying that a smaller magnet would need to be much stronger to observe significant effects.
  • A different viewpoint emphasizes that a larger magnet would produce a stronger magnetic field and that having magnetic field sources close together enhances the induced forces.
  • One participant provides a more detailed explanation involving Faraday's Law and the Ampere-Maxwell Law, describing how the time-varying magnetic field of the falling magnet induces a current in the tube, which in turn creates a magnetic field that opposes the motion of the falling magnet, consistent with Lenz's Law.

Areas of Agreement / Disagreement

Participants express differing views on the implications of magnet size, with no consensus reached on whether smaller magnets can effectively demonstrate Lenz's Law without being significantly stronger.

Contextual Notes

Some assumptions about the strength and size of magnets, as well as the specific conditions of the experiments, remain unaddressed. The discussion does not resolve the mathematical implications of the laws referenced.

gildomar
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In all demonstrations of Lenz's Law that I've seen about the falling magnet, the diameter of the magnet is roughly the same size as that of the tube. Would there be any difference if the magnet was significantly smaller?
 
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I think the proximity of the magnet to the metal helps the cutting of the magnetic flux. If you think of the extreme, a pea sized magnetic falling through a tube with a diameter of 1 meter would need to be VERY strong to see any effect. I am by far no expert though.
 
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The tube produces a magnetic field in response to the change in magnetic field from the falling magnet. To produce a large force, you want those magnetic field sources near each other, and that argues for a large magnet. Additionally, all other things being equal, you get a stronger field from a bigger magnet.
 
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More precisely the time-varying magnetic field of the falling magnet leads to an electromotive force, according to Faraday's Law,
$$\frac{1}{c} \dot{\vec{B}}+\vec{\nabla} \times \vec{E}=0.$$
This leads to a current in the tube (or coil). This current leads to a magnetic field, according to the Ampere-Maxwell Law,
$$-\frac{1}{c} \dot{\vec{E}}+\vec{\nabla} \times \vec{B}' = \frac{1}{c} \vec{j}.$$
The so "induced" magnetic field acts back on the magnetic moment of falling magnet in such a way to hinder it falling (Lenz's Law).
 

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