How would a spherical magnet with uniform density react?

Question

A spherical magnet with uniform density should, by common sense, correct me if I'm wrong, not have any favourable place, which it can call a pole. So, how is the pole of such a magnet defined? Also, how will the field lines behave? Will it show special behaviour or something?

Answer 1

The magnetic field of an object is a result of the magnetic domains within it lining up with each other and reinforcing each others magnetic fields.

When this happens it creates a preferred direction, i.e. it breaks the spherical symmetry, so your spherical magnet has a field aligned along some axis just like a bar magnet does. There is nothing unusual about the field from a spherical magnet; it is just a dipole field like the field from any other magnet.

The next question is what selects the axis along which the magnetic field forms? Suppose we heat the magnet to above its Curie temperature so it has no field. If we then cool the magnet we'll get magnetic domains forming spontaneously inside it. In principle the direction of these magnetic domains will be random, though in practice factors like the Earth's magnetic field or defects in the crystal structure of the sphere are likely to play some role.

Answer 2

What kind of "density" do you mean? If you mean magnetization density, which seems like the most natural sense in the context of magnetism, then magnetization density is a vector quantity which does pick out a specific direction, and points from the south pole to the north pole.

Answer 3

(I'm assuming you mean the domains are all pointing out, or all pointing in.)

To understand the answer, first know that the field at some distance away from a hollow sphere is the same as it would be if that sphere were condensed so it isn't hollow. For example, gravity near a planet is the same whether that planet is hollow or not, as long as it has the same mass.

So let's say your magnetic sphere is composed of north poles pointing out and south poles pointing in. Now with the knowledge from the previous paragraph, consider that the magnetic field above your sphere is just as affected by the north poles at the surface as it is by the south poles from inside. So the net field is zero above the surface of the sphere.