# Apparent extension of magnets

I was fiddling with my little sister's magnets just now and noticed that if I stuck one pole to a coin I can add a couple of coins/paperclips successively to make a chain, which doesn't really happen if there was no magnet

1)First of all, why does this happen?

2)Does the amount of links I can make depend on the magnet or the intrinsic properties of the metal?

3)why when I add an opposite pole to the topmost coin/link everything falls except the one on top (this was the one that weirded me out the most)

• I cannot understand your last query clearly, are the poles of the additional magnet like or unlike and where did you place it? Commented Oct 31, 2020 at 17:37
• @pranjalverma unlike, very close to each other near the top. Commented Oct 31, 2020 at 18:43

This problem is best thought of in terms of magnetic circuits, which are mathematically analogous to electrical circuits with current replaced by magnetic flux, voltage (or electromotive force) replaced by magnetomotive force (MMF) and electrical resistance replaced by magnetic reluctance.

The steel that the paper clips are made of is a magnetic material, characterized by high permeability. This means that the paper clips have low reluctance and allow magnetic flux to easily "flow" through, similar to wires in electrical circuits. The "source" that powers the magnetic circuit in this case is the magnet: you can think of it like a voltage source in electrical terms. The magnetic circuit can be simplified to look like the following "reluctance ladder", with the permanent magnet connected between points A and D, where A is the contact between the magnet and the first paper clip, and D is the opposite pole of the magnet.

(image from this question)

Each horizontal reluctance models a paper clip. Unlike typical electrical circuits, magnetic circuits are "leaky": magnetic flux doesn't remain confined to the paper clips. Magnetic field lines leak out and return to the magnet through the air. This is modeled by the vertical reluctances in the figure.

As you can imagine, as you add more paper clips to the chain, the magnetic flux in the last paper clips gets lower because of leakage flux. The force on the last paper clip is related to the flux in the last link. More accurately, the force is related to how much the total magnetic energy (outside the permanent magnet) increases as you add another paper clip. This energy is analogous to electrical power dissipated in the ladder. The longer the chain, the lower the change in energy and the lower the force on the last paper clip.

How many paper clips you can chain depends crucially on the magnet, which is the source of MMF. It depends both on its geometry and its magnetization curve, which is influenced by the material. Coercivity is one of the important parameters in this case: it determines the maximum MMF in high-reluctance magnetic circuits like this.

(magnetization curve example taken from here)

When you approach the first paper clip with an opposite pole, you are providing a low reluctance return path for the magnetic flux, effectively shorting everything that comes after the first paper clip. Moreover, this second magnet can force magnetic flux with opposite direction to flow in the other paper clips via leakage paths, partially cancelling the flux due to the first magnet. Thus these paper clips no longer influence the total magnetic energy significantly, and therefore aren't pulled by a strong force.

• What if there is only a single point of contact ? Can this effect still occur? Commented Oct 31, 2020 at 18:42
• Contact between what? The coins/paper clips?
– Puk
Commented Oct 31, 2020 at 18:43
• The magnet and the paper clip, In your circuit diagram it closes at A, what if it doesn't? will it close through air as you also mentioned? Commented Oct 31, 2020 at 18:45
• You can think of A as the point contact between the magnet and the first paper clip, and D as the opposite pole of the magnet. Magnetic flux enters the first paper clip at A, all of that flux eventually leaks out and returns to the magnet at D.
– Puk
Commented Oct 31, 2020 at 18:49

It is due to the ferromagnetic nature of iron paper clips in which magnetic domains in the paper clips get oriented along the magnetic field thus magnetising it . So amount of links depends entirely on strength of magnetic field .

Regarding your last query, I think it is related to the cancellation of magnetic fields thus weakening the strength.