Question

Magnetic field lines are always nearly normal to the surface of a ferromagnet at every point. (This fact is analogous to the static electric field lines being normal to the surface of a conductor at every point). Why?

Answer 1

Hint: We know that ferromagnets allow external magnetic field lines to pass through them. In such a case, think of how the field lines are incident on the magnet’s surface. As for the analogy, we know that the surface of an electric conductor inherently contains static charges at equilibrium. If there was an electric field along the surface of the conductor, think of what would happen when the charges experience a force. Would the charges still be static?

Complete Solution:
Let us begin by defining the term relative permeability $\mu_r$.

We know that when a magnetic material is placed in a magnetizing field, magnetic permeability $\mu$ helps us measure the material’s resistance to the ambient magnetic field. It measures the degree to which the external magnetic field can penetrate through the material.
Now, the ratio of the permeability of a medium to the permeability of free space is called the relative permeability. $\mu_r = \dfrac{\mu}{\mu_0}$. This also represents the ratio of total magnetic induction inside the material to the magnetic induction of the applied field, i.e., $\mu_r=\dfrac{B}{B_0}$.

Now, the relative permeability of ferromagnets is $\mu_r >>1$. This means that ferromagnets allow or pull in external magnetic field lines and allow them to pass through their material. This also means that the magnetic field lines find it easier to travel through the ferromagnet than pass through the free space surrounding it.

The key here is that the field lines travel “through” the material. This implies that they always travel normal to the surface of the ferromagnet and not along the surface. This is because the field B inside the material is much stronger than that of the magnetizing field $B_0$ due to the pulling in of a large number of lines of force with the field lines being uniform and parallel along the magnetic material.

Note:
In the same way, let us attempt to understand the reason why static field lines are always normal to a conductor surface. If this wasn’t the case, then the electric field would exert a force on the charges on the surface of the conductor which would render them non-static since they would move around. However, they would eventually redistribute in a way to attain a uniform charge distribution, where the electric field would only be normal to the surface, eliminating its tangential(surface) component.