1
$\begingroup$

If we hold two magnetic like-poles together and start to move them away, would the repelling force reach absolute zero at certain point?

In that scenario, as a layman, I think that there is something paradoxical :( We can never reach absolute ZERO in Physics. Theoretically, it will always be bigger than zero... it just gets smaller and smaller... ad infinitum. And that reminds me of Zeno paradox.

Improve this question
$\endgroup$
3
  • $\begingroup$ why would letting the magnets go apart cause the temperature to do to 0? $\endgroup$
    – shai horowitz
    Commented Aug 7, 2022 at 10:08
  • $\begingroup$ Not the temperature, but the repelling force between the magnets $\endgroup$
    – user342647
    Commented Aug 7, 2022 at 10:13
  • $\begingroup$ That's why fields fills each and every corner of universe. You are right that zero is "anti-infinity", i.e. $0=1/\infty$, so even being mathematically a number, i.e. "countable object", you can have them as many as you like in any real number set, without changing set total. So it's a bit strange concept this zero. I would rather say that you can't count what you don't have. You don't have $10$ or $10~000~000$ Ferrari ? Nobody knows. In this respect, indeed zero is a bit "unphysical". $\endgroup$
    – Agnius Vasiliauskas
    Commented Aug 9, 2022 at 21:03

2 Answers 2

Reset to default
1
$\begingroup$

Like gravity or electrostatic attraction, magnetism reduces with distance. However, while the first 2 have an inverse square law (the force diminishes with the square of the distance), the magnetic force diminishes with the 4th power of the distance, or $f\propto{r^{-4}}$. Hence it reduces much faster than electric or gravitational forces.

However, even if magnetism reduces very quickly, we still see that, no matter how large $r$ gets, the resulting force never reaches $0$

Improve this answer
$\endgroup$
0
$\begingroup$

The magnitude of the force between the two magnets will approach zero as they get further and further apart. It never (in theory) actually reaches zero because they are always a finite distance apart - we say the force approaches a limit of zero as the distance between them approaches (but never reaches) infinity. Of course, the force will eventually become too small to measure, so we might say it becomes zero for all practical purposes.

The term “absolute zero” is usually reserved in physics for a temperature that is so low that all molecular and atomic motion ceases. It is true that the laws of thermodynamics mean that this theoretical temperature can never be achieved in practice. However, many other physical attributes can (and do) become zero.

Improve this answer
$\endgroup$
5
  • $\begingroup$ At what number magnetic is considered as "zero for all practical purposes"? I understand that these are inevitable mathematical consequences, but it gets really vague in a sense :( $\endgroup$
    – user342647
    Commented Aug 7, 2022 at 10:59
  • $\begingroup$ @IvNik Obviously there is not a hard and fast cut-off, but even with laboratory equipment it would be very difficult to measure a force smaller than $10^{-10}$ N. If this practical limit is too vague then ignore it and stick with the theoretical statement that the force can become as small as you like, but is never actually zero. $\endgroup$
    – gandalf61
    Commented Aug 7, 2022 at 11:38
  • $\begingroup$ Thank you for the wonderful answers and explanations for layman. Is it "similar sort of thing" in quantum mechanics, when we say that "there's non-zero probability for a cup on the table to quantum tunnel"? I guess that is analogical example for approaching zero, as the case with the two magnets. Am i right? Or they are different stories? QM, of course, is probalistic. $\endgroup$
    – user342647
    Commented Aug 7, 2022 at 11:54
  • $\begingroup$ @IvNik To be honest I don’t see any connection between the two scenarios apart from the fact that they both involve quantities that are very close to zero. If you want to pursue this topic you should post a new question. $\endgroup$
    – gandalf61
    Commented Aug 7, 2022 at 13:00
  • $\begingroup$ These are two scenarios and in each of them we have an entity which we can't drive down all the way to zero. Now that is the "connection" between the two scenarios. In QM, the matrices that correspond to “allowed quantum processes” can never give you an absolutely zero output. It’s all about probabilities, and while you can drive entries in the density matrix down to tiny, tiny, tiny numbers, you can never get them all the way to zero. You can zero them “for all practical purposes,” but if you’re going to totally nit pick, then they’re not zero. See that?: ) $\endgroup$
    – user342647
    Commented Aug 7, 2022 at 14:37