Can somebody please explain what this physics question (Is the strenght of the magnetic field the same across the surface of the magnet's pole?) has to do with engineering? Is physics not about how nature (in this case magnets) works? Does it matter if I intend to use the answer towards engineering later on?
That was me. But I am always happy if the community votes to re-open a question that I've closed: it means the question is more interesting than I realized.
I left this comment when I closed the question:
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" that isn't a good fit for an answer in our format. People who need uniform fields build Helmholtz coils.
I stand by that. 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 fact that this meta response to your question is physics stories rather than site policy suggests that perhaps I wasn't right to have closed it. I'll let the folks in the reopen queue make that judgement. I think that a question tagged experimental-technique about how to determine whether the field you want is uniform would be okay for us. But you seemed to think that you were asking a basic question about magnetism, when you were in fact asking something sneakier about the fabrication and storage of "typical" consumer magnets. That's what prompted me to use the "engineering" close reason.