Magnetic fields - why not proportional to 1/d^2?

[chris661]

Hi guys,

I asked my A-level physics teacher why magnetic fields weren't proportional to 1/distance squared, and got the reply that "That's not how magnetic fields work" - I got the distinct impression he had no idea.
Figured I might as well try here.

Any ideas?

Cheers,
Chris

[mfb]

If you would have magnetic monopoles, their field would fall off with 1/r^2.
However, no magnetic monopoles were observed so far (apart from quasiparticles in solids), all known sources of magnetic fields are dipoles.
You can imagine a dipole as a system with a negative and a positive charge with a small distance in between. While both charges have a field of 1/r^2, they partially cancel each other, and the remaining field is only the difference between both, which is proportional to the derivative of 1/r^2 and therefore proportional to 1/r^3.
This is similar to electric dipoles.

[chris661]

See, now I'm more confused.

What you've said makes sense to me, but still doesn't fit with the equations we were using.

To put some context around it, the subject was the magnetic field around a very long current-carrying straight wire.

My thoughts are that, as you move further away, the area of the circle increases with the square of the radius. It's an area that's being magnetised (well, actually a volume, but we'll discount the 3rd dimension - along the length of the wire - for the sake of simplicity), so, as far as I can see, so the field strength ought to fall off with the square of the distance from the wire, yet this is not the case.

B=(u0*I)/(2pi*d)

where u0 = is the permeability of free space, 4pi * 10^-7
I = current through conductor
d = distance from wire
B = magnetic field strength

Still pondering,

Chris

[gmalivuk]

What do you expect the electric field to look like around a static charged wire?

[Quizatzhaderac]

A point monopole would work like a point charge or point gravity and fall off 1/d².

The wire is not a point, it occupies every point along one dimension. Since you're adding a dimension to the source, you take one aware from the dispersal.

The magnetic field isn't proportional to the area of the circle (in this case), it's proportional to the circumference of the circle.

With gravity or a charge coming from a point, it's inversely proportional to the surface of the sphere around the point, not the area.

You're probably thinking (in the case of the wire) it's like if you suddenly placed some water on a table. A time goes by, the water would form a larger circle, with the height of the water equal to the volume divided by the area of the circle formed. However, in this example the water in placed at one point in time and no more water is added. The wire is continuously producing a magnetic flux.

[chris661]

Think I get it now, thanks Quizatzhaderac.

I suppose, going back to my audio background, its a column source (where SPL drop is 3dB (=half energy) per double of distance) as opposed to point source, which does follow an inverse square law.

[gmalivuk]

Exactly.