Is 1/R^3 descriptive of magnetic force drop off?

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Discussion Overview

The discussion revolves around the behavior of magnetic forces, specifically whether the drop-off of magnetic force can be described by a 1/R^3 relationship at large distances from a magnetic dipole. Participants explore concepts related to magnetic fields, the transition from near-field to far-field behavior, and the implications of these ideas in the context of existing literature and experimental setups.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • Some participants assert that the magnetic field strength of a dipole decreases as 1/R^3 at far distances, while a monopole would decrease as 1/R^2.
  • Others question the definition of "far field" and the conditions under which the 1/R^3 behavior applies, suggesting that the transition point is not clearly defined.
  • A participant expresses surprise at the 1/R^3 relationship, noting it is not commonly found in educational materials.
  • Some participants discuss the implications of the magnetic force drop-off in relation to gravitational forces, highlighting the differences between attractive and repulsive forces in magnetism.
  • A participant presents a graph illustrating the transition from 1/R^2 to 1/R^3 as one moves away from a magnetic dipole, suggesting a gradual change rather than a sharp boundary.
  • Concerns are raised about the validity of the experimental setup shown in the referenced YouTube video, with some participants suggesting it may be faked.
  • There is a mention of textbooks that describe the far-field behavior of dipoles, with a participant referencing a specific textbook that derives the 1/R^3 relationship.

Areas of Agreement / Disagreement

Participants express a mix of agreement and disagreement regarding the drop-off behavior of magnetic forces. While some support the 1/R^3 relationship, others challenge the clarity of definitions and the applicability of this model in different contexts. The discussion remains unresolved with multiple competing views present.

Contextual Notes

The discussion highlights the lack of consensus on the transition point between near-field and far-field behaviors, as well as the dependence on specific definitions and conditions. There are also references to varying interpretations in educational resources.

Who May Find This Useful

Readers interested in the nuances of magnetic field behavior, the mathematical modeling of forces, and the implications of experimental setups in physics may find this discussion relevant.

rockyshephear
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Someone on YoutTube stated...

Each magnetic pole drops off by 1/R^2. Once you get away from both poles (Cavendish setup) they they start canceling each other out and it ends up as 1/R^3.

Comments?

Here's the link if you need backup info
http://www.youtube.com/comment_servlet?all_comments&v=euvWU-4_B5Y
 
Last edited by a moderator:
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Yes, that's correct. Far field magnetic strength decreases as the cube of the radius.
 
What do you mean by far field magnetic strength? And can the setup on the youtube page work like it depticts?
 
I've never seen this equation ever!
 
The field strength of a magnetic dipole drops off as 1/r^3 when you're relatively far away from both poles.

A magnetic monopole's field strength would drop off as 1/r^2, but there are no true magnetic monopoles (as far as anyone knows), so the leading-order contribution is the 1/r^3 term.
 
So, I guess I have to forget what I've read that magnetism of a metal object near a magnet (always a dipole) fades off with the square of the distance. Have they started changing the textbooks yet? lol
 
Relatively far away from both poles. Like a million miles? How do I know the tranistion point? So the force varies like this?

R being 1 inch = 1 N, 2 inch =1/4 N, 3 inch = 1/9 N...(somewhere it changes)...1 mile = 1/R^3
 
Can someone look at the YouTube video and indicate whether this is a faked setup or not?

http://www.youtube.com/comment_servl...&v=euvWU-4_B5Y
 
Last edited by a moderator:
rockyshephear said:
So, I guess I have to forget what I've read that magnetism of a metal object near a magnet (always a dipole) fades off with the square of the distance. Have they started changing the textbooks yet? lol
Ah, but you're talking about near a magnet. When you're much closer to one pole of a magnet than the other pole, then it is a 1/r^2 force (or, well, very nearly so) because the effect of the one pole you're close to is so much larger than the effect of the other pole. The 1/r^3 behavior is only far away from the dipole.

If you were to start next to one pole of a bar magnet and move away in any direction, measuring the magnetic force as you go, you'd find that it starts out looking like 1/r^2 and then gradually transitions to 1/r^3.
 
  • #10
Wow, I have never ever read this anywhere and even in the MIT Walter Lewin lectures either. I'm amazed. Please check out the YouTube video and comment. Thanks. I was wrong.
 
  • #11
I made a little graph to show the magnetic force dropoff from a dipole, as you start from one pole and move off to the side. The red line is the actual dipole force, the green line is 1/r^2, and the blue one is 1/r^3, and you can see that the red line starts out following the green line then "moves over" to the blue line. As I said, it's a gradual transition, but the center of sorts is at r=1 on the graph, which represents the length of the dipole. So if the two poles are a distance d apart, roughly speaking, the force is like 1/r^2 if you're closer than d, and like 1/r^3 if you're further away than d.

Technical details: I actually used the formula for an electric dipole,
\vec{E} = \frac{q}{4\pi\epsilon_0}\left[\left(\frac{1}{x^2}-\frac{x}{(x^2+d^2)^{3/2}}\right)\hat{x} - \frac{d}{(x^2+d^2)^{3/2}}\hat{y}\right]
but a magnetic dipole behaves the same way with respect to r.
 

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  • #12
rockyshephear said:
Wow, I have never ever read this anywhere and even in the MIT Walter Lewin lectures either. I'm amazed. Please check out the YouTube video and comment. Thanks. I was wrong.

Haha that youtube video is definitely faked somehow. The gravitational constant is far far far too weak to have such an effect.
 
  • #13
So why does not gravity do the same thing??
 
  • #14
Because gravity is universally attractive. There are no gravitational poles. However, note that tides, which are ultimately caused by gravity, do also decrease with the radius cubed because tides are a differential force.
 
  • #15
Thanks!
 
  • #16
rockyshephear said:
So, I guess I have to forget what I've read that magnetism of a metal object near a magnet (always a dipole) fades off with the square of the distance. Have they started changing the textbooks yet? lol

Which textbooks say this? Last semester I taught intermediate level E&M from https://www.amazon.com/dp/013805326X/?tag=pfamazon01-20 which derives the far field from both electric and magnetic dipoles as 1/r^3.

See also for example Wikipedia's article on dipoles.
 
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  • #17
What's the equation to determine how far away the far field is?
 
  • #18
See Diazona's answer in post #11. There's no sharp "boundary" between the near field and the far field. The far-field formula is always an approximation to the true field, which gets better and better as you get further and further away from the dipole.

How far away you have to get before the far-field formula is "good enough," depends on your definition of "good enough."
 
  • #19
Is it like this? Since gravity is totally attractive and magnetism has attractive and repulsive attributes, the attractive and repulsive tend to cancel each other?
Also can you check the link to YouTube and tell me if this setup if faked?
 

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