# Splitting a bar Magnet Lengthwise

Q:
I dropped a bar magnet and broke it. It wouldn't fit back together again because it broke length wise, frome north to south. If the poles of the two pieces lined up with each other before they broke, what keeps the magnet together to begin with? If they repel now, why didn't they before it broke?
- Michael French
Napavine Washington, U.S.A
A:
Good question.   There are two ways to think about it.  As you know, like magnetic poles repel each other and unlike poles attract.   When you try to put them back together, the two poles of each magnet repel each other.  The reason the magnet doesn't fall apart to begin with is that the strength of the material is strong enough to overcome the repulsion.   If you cut a bar magnet crosswise, the two pieces will cheerfully attract each other because they are of opposite sign.

The other way of looking at it, a bit more obscure perhaps, is that there is an energy density associated with magnetic fields.  It's a bit complicated but the essential point is that the total energy is proportional to the square of the magnetic field integrated over space.  The total energy of the two halves put together is more than twice the total energy of the two halves separated far apart.  So there will be a force pushing them apart.

LeeH

(published on 03/21/2010)

## Follow-Up #1: when do broken magnets repel?

Q:
I've tried seven or more time to get past the captcha hurdle but I fail every time. Here's my question: I have 3 "refrigerator" magnets. (about 1 inch dia.) One of them recently broke into two C-shaped pieces. When I try to put the two pieces together, as they were before breaking, the two pieces repel each other. When I reverse one piece, they attract, but of course the mating surfaces do not match. When I put the two pieces together on the refrigerator door in the positions where the mating surfaces match, they stick to the door (stilling repelling each other) separated by about 1/4 inch. I note however, when two straight magnets are cut, the cut ends have opposite polarity and still attract each other. Please can you explain why the toroidal magnets behave this way? Thanks, -p-
- paul (age 62)
Lexington MA
A:

Two magnets placed side-by-side repel if their fields point the same way. Placed end-to-end, they attract if the fields point the same way.

For bar magnets, it's true that if you break them in half across the small dimension, the halves attract, If you break them in half lengthwise the halves repel unless you line them up end to end.

The magnetic field in your broken magnet must have pointed approximately in the plane of the broken surface.

Mike W.

(published on 07/14/2013)

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