# Question about magnetic fields and magnetic forces

Hi all,

I'm currently working on a game about magnetism and have run into some problems. I'm hoping that you guys here will be able to help me with it.

I've been reading about magnetic phenomena on the net, and one of the things I've found is that the magnetic force exerted between two unlike poles is inversely proportional to the distance between them squared. If that's the case, then when two poles on a bar magnet are touching, shouldn't the force they are exerting on each other be infinite since x/0 = ∞?

Also, another question I'm wondering about is this: if a strong magnet that is smaller in mass pulls a paramagnet towards itself with a vector V, does it experience an opposite vector -V? Or does it just experience the force that the induced pole on the paramagnet exerts on it?

Thanks to anyone who might be able to help!

mfb
Mentor
and one of the things I've found is that the magnetic force exerted between two unlike poles is inversely proportional to the distance between them squared
This is an approximation for magnet distances much larger than the magnet sizes. As you can see, this approximation is bad for a distance close to zero.

>> if a strong magnet that is smaller in mass pulls a paramagnet towards itself with a vector V, does it experience an opposite vector -V? Or does it just experience the force that the induced pole on the paramagnet exerts on it?
Why do you think the two are different?

>> if a strong magnet that is smaller in mass pulls a paramagnet towards itself with a vector V, does it experience an opposite vector -V? Or does it just experience the force that the induced pole on the paramagnet exerts on it?
Why do you think the two are different?
It seems to me that when a strong electromagnet pulls in a mass greater than itself no counter force acts on it.

mfb
Mentor
Newtons third law
And if you have a strong magnet, you can easily test this. It will stick to everything where it can induce a magnetic field.

Ah thanks, I didn't know Newtow's third law applied to fundamental forces. Another thing: how do I get a good magnitude of the force exerted between two objects? Is (StrA+StrB)/Dist^2 a good estimation?

Ah thanks, I didn't know Newtow's third law applied to fundamental forces. Another thing: how do I get a good magnitude of the force exerted between two objects? Is (StrA+StrB)/Dist^2 a good estimation?

1. You should not add the fields. The magnet's own field does not contribute to the force
2. The force depends on the areas too. The force between two narrow magnet bars at the is smaller than the force between two thick ones with the same distance

1. You should not add the fields. The magnet's own field does not contribute to the force
Isn't the force derived from the sum of the two fields interacting with each other?

Isn't the force derived from the sum of the two fields interacting with each other?

I haven't seen such a derivation. If by "Str" you mean the magnetization (M) of the magnets which is a constant vector for a permanent magnet, then the force between two permanent magnets is somehow proportional the products of the components of two magnetizations M1 and M2.

A more intuitive way of finding the force is to calculate the force on the surface current of one magnet due to the field of the other magnet. The current is equal to $J_{s}=\vec{M} \times \vec{n}$ with $\vec{n}$ being the outward normal to the surface of the magnet. Now the surface force density becomes

$f_{s}= (\vec{M} \times \vec{n} ) \times \vec{B}$

Here only B due to the other magnet contributes because the own field vanishes due to the cross product . Again we have the force as the product of the two magetizations because B is proportional to the magnetization of the other magnet.

One more thing: the magnetic moment that each magnet exerts on another is equal and opposite too right?

I'm not sure what you mean. When a small piece of iron is placed near a pole of a permanent magnet, the magnetic dipole moments in the iron are aligned and make the iron a temporary magnet and with a polarity that the force is always attractive.

For between two permanent magnets, it's different because the dipole moments already aligned and can be changed. Hence depending on polarity, we have attractive or repulsive force.

But if you are asking about the torque exerted on each magnet, I am not sure whether they are equal or not. Forces are equal though.

Well technically one thing never touches another thing(excluding nuclear reaction which i do not know much about).
and idont think that it works the same way at electronic level , you have to consider the shape and orientation of orbitals and everything ,anyways in your case we don't even come close to that level and there is still a large distance (with respect to atomic level) between the magnets.