Magnetic field strength at a distance

[noname12345]

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 ?

 

[Dale]

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.

I know approximates to 1/r^3,

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

 

[noname12345]

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.

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.

 

[Dale]

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.

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.

 

[noname12345]

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.

 

[Dale]

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.

 

[CWatters]

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.

 

[noname12345]

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.

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?

 

[CWatters]

Ok my bad. With an infinitely large magnet it will as near to 1T as makes no difference. Infinity >> 1mm.

 

[noname12345]

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?)

 

[CWatters]

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.

 

[CWatters]

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.

 

[noname12345]

or something like that

great. thanks.

 

[CWatters]

Looks like a formula down here but I've not looked at its origin or checked under what conditions it's valid..

https://www.supermagnete.de/eng/faq/How-do-you-calculate-the-magnetic-flux-density

Perhaps you can work the numbers to see how near 1T it will be.

 

[Dale]

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.

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