Consider the following configuration:

Will the two blocks of iron (in the image) experience the same magnetic pull (one being in the center and the other closer to the edge of the pole's top surface)?

Are the magnetic field "lines" evenly distributed across the pole?

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    $\begingroup$ I think the more number of magnetic field lines the stronger the force but that's my naive thinking hee hee. $\endgroup$ – user6760 Dec 16 '18 at 6:47
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    $\begingroup$ This question is the subject of a meta discussion. $\endgroup$ – rob Dec 27 '18 at 5:33

The magnetic field strength usually varies across the face of a pole of a bar magnet. The attraction does not depend on the magnetic field strength (what you refer to as the "number of lines"). It depends on the gradient of the field strength. So if the field strength is uniform in the vicinity of the blocks of iron, then there is no net force on the blocks (though the blocks might experience a torque). If you put a piece if iron in a field whose lines are converging, the iron experiences a force in the direction toward which the field lines converge. Note: magnetic field lines per se do not exist. They are a useful way to visualize the field, but are not real. What does exist is a field direction and magnitude at each point. In the region near the pole of a bar magnet, the "lines" converge toward the pole pretty much the way you have drawn them.


This isn't a fundamental property of a permanent magnet: it depends on details of the materials used in its manufacture, on the process by which it was magnetized, by its history of exposure to other magnetic fields, and a bunch of other "weather." People who need uniform fields build Helmholtz coils.

It's probably possible to build a magnet with a uniform magnetization over the surface. It's definitely possible to build a magnet where the magnetization is not uniform. And it's possible to take a uniformly magnetized hunk of stuff and screw it up.

I used to teach a poorly-designed lab experiment with solenoids and a bunch of old AlNiCo magnets, where the students had a 10% chance of accidentally reversing the polarity of their bar magnet with the solenoid. By the end of the week, when all dozen intro lab sections had learned on the same equipment, I would usually spend an afternoon re- polarizing the magnets so that they matched their labeling, and I would usually discover one magnet that some students had converted into a quadrupole! Switching to the newer rare-earth magnets reduced the chance of an accidental mispolarization, but didn't eliminate it.

That's before we start to talk about the "patch effect" in polycrystalline metals. The patch effect is usually important in precision electrostatics experiments (for example): parts of a metallic surface which present different crystal planes have different work functions, so there is some non-removable variation in the electrical potential across the surface. I haven't encountered a discussion of the patch effect in surface magnetism, but the phenomenon of magnetic domains is clearly closely-related.

As a rule of thumb, if you want your magnetic field to be uniform over some length scale $\Delta x$, then the distance between your should-be-uniform field region and you magnetic field source should be several times larger than $\Delta x$. There is a nice mathematical technique for estimating just how much larger.


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