Magnetic field lines at the center of the magnet pole, how do they look like?

Question

Magnetic field lines are loops, so at the surface of a magnet pole they look like this? there is a dead zone at the center where there is no lines/magnetic field present?

Or lines converge in the middle to a single line or point? like so?

Which picture is correct? also on some googled pictures I can see a single straight line coming from the center of the pole that goes nowhere... I know that lines are really an mathematical artifact, I just want to know how the field is shaped near the surface at middle of the magnetic pole.

Answer 1

You can model a magnet as a uniformly magnetised material. This allows you to solve for the magnetic field everywhere using magnetostatics.

For a general geometry this is not possible to do analytically, but you can always compute it numerically. You can start to build intuition from simple geometries like the magnetised ball which is doable analytically. In this case there is no deadzone inside (i.e. the field does not cancel), but is rather constant: $$ H = -\frac{1}{3}M \\ B = \frac{2\mu_0}{3}m $$ with $M$ the uniform magnetisation inside the ball, $B$ the magnetic field and $H = \frac{1}{\mu_0}B-M$.

In general, the magnetic field lines continue inside the magnet but are bent by the surface currents in this ideal setting. However, unlike the magnetised ball, the field is typically not constant and has a more complicated expression. In general, since you cannot have magnetic monopoles, your field lines cannot just suddenly end.

Hope this helps.