How do magnetic shields work?

I've come across the fact that magnetizable material can shield magnetic fields. For example, if I put a ferromagnetic plate between the magnet and a nail that is hanging on a thread pulled towards the magnet, the nail will eventually fall down when the plate covers the path between them. How exactly does this work? The descriptions I've found via google so far don't make sense to me. Probably there is a difference between static and dynamic fields, I'm mostly interested in the static case though.

The intensity B of the magnetic field, given a fixed position, is proportionnal to the inverse of the permeability $\mu$ of the material. However, $\mu = \mu_0\mu_r$ where $\mu_0$ is the permeability of the void (it is a constant) and $\mu_r$ is the relative permeability of the material. Then,

$$B \propto \frac{1}{\mu_r}$$

However, for air, $\mu_r \approx 1$, and for iron or ferrite (and many other materials) it can be more than 1000, which strongly diminish the intensity of magnetic field.

• Thank you for your answer. I'm not sure if I got it correct though: I see that $\mu_r \approx 10^4$ is a reason for the field intensity to decrease. But only inside the material, right? The field behind the plate should still have the same intensity which is not the case. – user424862 May 14 '17 at 12:02
• The material acts like a shield (like when using your phone on a tunnel: the electromagnetic signal can't go through the mountain you're under, but it can travel through air; however, it can't escape the tunnel), so event after the plate, the field is weaker. – Spirine May 14 '17 at 13:04
• That was exactly my question: WHY is it weaker? Only because there is one spot where the field intensity decreases because of some material, the field won't be globally weaker instantly, or am I mistaken here? – user424862 May 14 '17 at 13:41
• To find the electromagnetic field caused by a source on a given point, you can use quantum electrodynamics. According to this theory, you have to integrate along all the possible path that go from the source to the given point to find the resulting field. Here, you can see the the field on a given point depends on the whole space configuration. However, I couldn't tell you more than that about this topic. – Spirine May 14 '17 at 13:47
• Oh wow, that's interesting! I was hoping for some kind of comprehensible phenomenological explanation rather than an abstract theory. But I guess there is none so I think I'm okay for now. Thanks for helping! – user424862 May 14 '17 at 13:53

Perhaps you know that magnetic fields are closed loops. So if you influence such a magnetic field by another material the magnetic field lines take a different path.

I've come across the fact that magnetizable material can shield magnetic fields.

Any material is magnetisable but in different strength. This has to do with the magnetic dipole moments of the subatomic particles of the material. If the particles could be aligned easily - like this is the case for ferromagnetic materials -the field lines are going along the shape of this material and in some regions outside the shape the magnetic field gets very weak or is not observable at all. By this

the nail will eventually fall down when the plate covers the path between them.

• Thank you for your answer as well. But unfortunately you didn't really explain what I was asking for. So let's say the field lines are following the shape of the material. Why would the intensity then decrease outside of the material? To me, changing the direction of the lines doesn't implicate a decrease in intensity. But I'm clearly not an expert so I would be glad if someone could elaborate. – user424862 May 14 '17 at 12:53