Why is a magnet broken in half still as magnetic as the original?

[holly]

Q. A rectangular bar magnet is broken in half longways. The resulting pieces are:
Answer: as magnetic as the original magnet.

I don't see why it isn't half as magnetic. I broke one of my fridge magnets in half, and I'm tellling you, it's only half as strong now. It can't hold the recipe up on the door anymore.

My professor says my experiment is invalid, but won't say why. Is it really as "magnetic" as the original magnet? It sure seems only half as strong.

Thanks for any insight.

 

[TheDude710]

Hmm, I think it is half as magnetic but you must prove it. Your professor might just mean that your argument is invalid but the conclusion is true.

 

[holly]

Thx Dude, maybe that's what my professor meant.

Now, if only cookiemonster, turin, or ShawnD, Doc Al, or the mysteriously absent marcus were around, we'd get a definitive answer! And all the nauseating math and physics to back it up...blech...maybe a minor miracle will occur and the answer will be here by morning...HINT HINT

 

[cookiemonster]

Huh? Oh, I suck at E&M. Sorry.

Maybe it's got somethin' to do with the charge density remaining constant?

Edit: Come to think of it, I think that might actually be it.

cookiemonster

 

[quantum mechanic]

Holly,

You are correct in that the strength of the magnetic field produced by the pieces of the original magnet is proportional to the change in size of each piece; therefore, a magnet broken in half would produce two magnets equal to half the magnitude of the original magnet, and each magnet would contain its own north and south pole.

 

[Doc Al]

Q. A rectangular bar magnet is broken in half longways. The resulting pieces are:

Oops... I just saw this one. Sorry, Holly.

I agree with quantum mechanic. The key is that you are dividing the magnet longways, which I interpret as right down the middle from North pole to South pole. It's the microscopic magnetic domains that add up to give the magnet its strength. You are splitting them into two pieces, each with half the strength.

A more interesting question is what would happen if you cut the magnet in half not longways, but across the middle between the north and south poles. Are you sure that's not what your professor meant?

 

[turin]

The quality of being "as magnetic as" something does not lend itself to quantitative analysis.

I will assume that it refers to the active property that a magnet has to attract ferromagnetic (and paramagnetic?) material. Magnetism is a funny thing, though. There is no such thing as a magnetic charge (so far as has been discovered in the more than 100 years of looking for it), so there isn't a good way to say that a chunk of stuff that attracts ferromagnetic material is magnetically charged.

Probably the best thing you can do is describe the magnetization of the material, that is, the amount of flux density that exists in the absense of an externally applied field. It does not good to speak of the amount of total flux because, on the one hand it is ambiguous how large of a region to consider, or, on the other hand, if you consider any closed surface, the total flux will of course be zero (by "law"). The flux density, being a density, is an intensive property. This is a fancy way of saying that every part of the system (assuming uniformity, homogeneity, isotropy, and all the other great assumption that we can't live without) contains that property the same as the whole regardless of how small a part one considers (assuming the system is a continuum).

So, if we assume that the bar magnet is a continuum of uniform, homogeneous, isotropic material that has a uniform, homogeneous, and isotropic magnetisation to begin with, then any piece of this magnet (assuming that we do not destroy any of our beautiful assumption in the act of sundering) will have the same magnetisation, magnetisation being an intensive property.

 

[holly]

*sniff*

I missed it on the test...alas, the words of wisdom, which I could have repeated parrot-like, since it's all beyond me, came too late, too late...

Woe, woe is me...

But I still got a 97, ha ha HA! High grade, high grade!

ALL THANKS TO THE GREAT BRAINS who have been so kind to me, so generous...

Guys, please see my "goodbye" in the general forum...