Magnetic field strength at a distance

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Discussion Overview

The discussion revolves around the magnetic field strength produced by a flat, infinite magnet and how it behaves at a distance from its surface. Participants explore the theoretical implications of magnetic field strength, particularly in relation to distance, and the differences between infinite and finite magnets.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant asks about the magnetic field strength 1mm away from a flat magnet with a surface strength of 1 Tesla, expressing confusion over the expected reduction in field strength.
  • Another participant asserts that the magnetic field strength remains exactly 1 Tesla at that distance, claiming that the field does not reduce with distance for an infinite flat magnet.
  • Some participants challenge the assertion that the field strength does not decrease, emphasizing the importance of geometry and the distinction between infinite and finite magnets.
  • There is mention of different decay rates for magnetic fields from various sources, such as dipoles and monopoles, with some participants referencing the 1/r^3 law for dipoles.
  • A participant suggests that for a finite magnet, the field strength will differ at various distances, but the differences will be small when close to the surface.
  • Another participant expresses uncertainty about the calculations needed to determine the field strength at different distances, suggesting that empirical measurement may be necessary.
  • One participant references a formula related to magnetic flux density but does not verify its conditions of validity.

Areas of Agreement / Disagreement

Participants do not reach consensus on the behavior of the magnetic field strength at a distance from the infinite flat magnet. Multiple competing views are presented regarding whether the field strength remains constant or decreases, and the discussion remains unresolved.

Contextual Notes

Participants highlight the dependence of magnetic field behavior on the geometry of the magnet, with some suggesting that the 1/r^3 law may only apply under specific conditions related to the size of the magnet compared to the distance.

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Hopefully, a simple question with a simple answer.

I have a flat magnet (assume infinite long and wide) with a field strength at the surface of (for simplicity) exactly 1Tesla.

What will the field strength be (in air) 1mm away from that surface?

I know approximates to 1/r^3, but 1/0.001^3 = 1e9.

The field strength will reduce, so ?divide? 1T / 1e-9; obviously not! It reduces, but not that fast.

So, what then? A formula and worked example would be very helpful.

Thanks, Buk.

Update: I found this formula: B = µ0 / 4π * 2µ / d3

d= distance in meters; µ0 = 4πe-7; and µ is defined as "the magnetic moment"; but no further explanation.

Is that a universal constant (like µ0) I can look up; or a constant to do with ?
 
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Buk said:
I have a flat magnet (assume infinite long and wide) with a field strength at the surface of (for simplicity) exactly 1Tesla.

What will the field strength be (in air) 1mm away from that surface?
Exactly 1 Tesla.

Buk said:
I know approximates to 1/r^3,
This is for a dipole, not an infinite flat magnet.
 
Dale said:
Exactly 1 Tesla.

So according to that, magnetic field doesn't reduce with distance!

So why doesn't every paper clip zoom off to the nearest magnet -- even if its a mile away? You obviously know that is twaddle.

Dale said:
This is for a dipole, not an infinite flat magnet.

I neither know, nor care what I "dipole" is; nor does the word impress me.

Review of your help so far: Not useful.
 
Buk said:
So according to that, magnetic field doesn't reduce with distance!

So why doesn't every paper clip zoom off to the nearest magnet -- even if its a mile away? You obviously know that is twaddle.
Because the nearest magnet is not an infinite flat plane. I am sorry if you don’t like the answer but that is the correct answer to the question you asked. The geometry matters.

Buk said:
I neither know, nor care what I "dipole" is
OK. That attitude seems counter productive to me, but best of luck in your educational pursuits anyway.
 
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Dale said:
Because the nearest magnet is not an infinite flat plane. I am sorry if you don’t like the answer but that is the correct answer to the question you asked. The geometry matters.

I specified the geometry.

I don't need the answer to a question you know the answer to; nor the question you think I should have asked, but the question I actually asked.

Anything else is a waste of my time and yours.
 
Buk said:
I specified the geometry.

I don't need the answer to a question you know the answer to; nor the question you think I should have asked, but the question I actually asked.

Anything else is a waste of my time and yours.
The question you actually asked is exactly what I answered with the geometry you specified.

The field from an infinite plane does not fall off. The field from an infinite wire falls off as 1/r. The field from a monopole would hypothetically fall off as 1/r^2. The field from a dipole falls off as 1/r^3 and so on for higher multipoles.
 
Not with that attitude.

Dale is correct. If you look at the field lines from a normal size magnet they diverge and loop around to the other pole, but near the center line and close to the pole they are straight and parallel. The wider the magnet and the closer you get to the pole the straighter the field lines get. With an infinitely wide magnet and very close to the pole there will be virtually no reduction in strength.
 
CWatters said:
virtually no reduction in strength.

He didn't say "virtually no reduction", nor "very little reduction" nor "an immeasurably small reduction". He said: "Exactly 1 Tesla".

So, let's try this another way.
FieldFallOff.jpg


As you don't like infinite, let's say the magnet is , oh, 5m in diameter. The ball is 1mm diameter positioned above the exact center.

At the point on the surface, 1mm below the ball, the magnetic field is determined to be EXACTLY 1 Tesla. A reading Newtons (calibrated to exclude gravity acting on the ball and the pivoting arm) is taken.

The drop arm is shortened to move the ball say (say) 10mm away. Another reading is taken.

Repeat at 20mm, 30mm 40mm...

Will they be different?
 

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  • FieldFallOff.jpg
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Ok my bad. With an infinitely large magnet it will as near to 1T as makes no difference. Infinity >> 1mm.
 
  • #10
CWatters said:
as near to 1T as makes no difference.

No difference to what?

Are you saying the difference is incalculable? (Or just that you/he don't know how to calculate it?)
 
  • #11
Buk said:
He didn't say "virtually no reduction", nor "very little reduction" nor "an immeasurably small reduction". He said: "Exactly 1 Tesla".

So, let's try this another way.
View attachment 221621

As you don't like infinite, let's say the magnet is , oh, 5m in diameter. The ball is 1mm diameter positioned above the exact center.

At the point on the surface, 1mm below the ball, the magnetic field is determined to be EXACTLY 1 Tesla. A reading Newtons (calibrated to exclude gravity acting on the ball and the pivoting arm) is taken.

The drop arm is shortened to move the ball say (say) 10mm away. Another reading is taken.

Repeat at 20mm, 30mm 40mm...

Will they be different?

Yes they will be different but the difference will still be very small.

I think the 1/r^3 law only applies when the distance is more than ten times the magnet diameter or something like that.
 
  • #12
Buk said:
Are you saying the difference is incalculable? (Or just that you/he don't know how to calculate it?)

No I don't know how to calculate it. I suspect you might have to measure it.
 
  • #13
CWatters said:
or something like that

great. thanks.
 
  • #15
Buk said:
He didn't say "virtually no reduction", nor "very little reduction" nor "an immeasurably small reduction". He said: "Exactly 1 Tesla".
For an infinite plane it is exactly 1 T. In order for it to be anything else the magnetic field lines would need to curve. But since it is an infinite plane then by symmetry they cannot curve. Therefore it is exactly 1 T.
Buk said:
As you don't like infinite, let's say the magnet is , oh, 5m in diameter. ... Will they be different?
For this finite magnet they will be different. If the magnet is short compared to the 5 m width then you can treat it as a loop of current. Otherwise you would treat it as a finite solenoid.

http://web.mit.edu/viz/EM/visualizations/coursenotes/modules/guide09.pdf
 

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