What force does a magnetic field of a certain strength apply to an object?

Question

Disclaimer: This question is mostly to fact-check an "Elementary" episode and is not home work related at all. For the curious, in that episode, a "20 tesla magnet" is used to propel bullets inside an elevator to produce gunshot-like wounds in people using the elevator by having the bullets deposited in the opposite wall be pulled in by the magnet.

From looking around on the internet and stack exchange, I expect this question to not have a trivial answer, but the lack of any real formulas that could reasonably be used surprises me a bit, so my question is two-fold: Is it impossible to answer a question like this given the data I'm about to provide, and if so, what other data is needed - or alternatively, what is the answer?

The question is: Given an electromagnetic field strength of 20 Tesla produced by an electromagnet (roughly barrel-sized according to the story), what force would be exerted on a bullet (let's say made of pure iron - take the most common isotope if that matters, and let's say its weight is 10g) in a distance of x meters from the magnet (take the optimal orientation of the magnetic flow)? What speed could be reached if the traveling distance of the objects is, let's say, 2 meters?

Edit to add: If need be, assume a spherical bullet. This is assuming that results will stay within an order of magnitude or two.

Answer 1

The reason that the forces in magnetic systems are hard to calculate is that there is no such thing as a magnetic charge.

Consider an analogous setup with an electric field. If we create an electric field of strength $E$ (in volts per metre) then if we put a charge $Q$ in the field the force on the charge is just given by $F = EQ$. Easy.

But if we create a magnetic field of strength $B$ then, because there is no magnetic charge, objects in the magnetic field experience no force and won't be attracted or repelled from the magnet. And this is of course mostly true. If try to pick up objects with a magnet then the vast majority of them don't respond at all. The very few objects that are attracted to a magnet are those made of a ferromagnetic material.

The reason that ferromagnetic materials will react to a magnetic field is because the magnetic field induces a magnetic dipole in the object. So we're not dealing with the force on a magnetic charge in a magnetic field, we're dealing with the force on an induced magnetic dipole in a magnetic field. But in a constant magnetic field the force on an induced dipole is zero. The reason why magnets attract things is because the magnetic field is not constant - it's high near the magnet and low far from it, and it's this variation in the field that creates the attractive force.

So let's consider your lift. If the magnetic field was a constant 20 Tesla then nothing in it would move because the net force on a dipole in a constant field is zero. You would have to arrange some setup like the field varying from 20T to zero across the lift, either from side to side or from top to bottom depending on which way you want the bullets to move. Then you would have to know the coercivity of the bullets so you could work out the strength of the induced dipole. Then, and only then, could you work out the force on the bullets.