# Magneto and Momentum

There’s this grim and affecting scene in both X-Men and X-Men: First Class – a young Erik Lehnsherr watches his family hauled away by Nazis through the gates of a concentration camp. He’s being dragged away by the Nazi guards, and he uses his magnetic powers for the first time to grab the gates with his burgeoning magnetic powers. The combined efforts of the guards aren’t sufficient to pry him loose and they finally have to club him over the head. We’ll call this Comic Book Physics Paradigm 1:

Later on, as the adult Magneto, he shoves around gigantic satellite dishes and picks up submarines while standing in an airplane and generally doesn’t bother to obey Newton’s third law. We’ll call this Comic Book Physics Paradigm 2:

Paradigm 2: no Newton's 3rd Law

The third law is the one that says “For every action there is always an equal and opposite reaction”. That’s a pretty good statement of physical reality as it was known in Newton’s time, but today we usually express the same concept in terms of conservation of momentum generally. There’s a reason for this. Fields – such as magnetic fields – can themselves carry momentum and it’s difficult to think of fields in terms of point forces.

The force from a magnetic field is one of the big equations that’s relevant in first-year physics, so let’s write it down:

$latex \displaystyle \mathbf{F} = q \mathbf{v} \times \mathbf{B}$

The force on a charge q is proportional to the magnetic field B, but also to the velocity v of the particle. If you’re not yet familiar with vector notation, that little multiplication symbol is a vector cross product symbol. The result of the cross product of two vectors is itself a vector, and points in a direction perpendicular to both original vectors. This is pretty weird. A charged particle in a magnetic field doesn’t feel a force unless it’s moving, and even then that force doesn’t point along the field.

So how is it that Magneto (or refrigerator magnets, for that matter) can pull metal objects along the field lines? Well, they can’t. It turns out (and we’ll derive it in a later, more technical post) that magnetic fields don’t attract objects. Gradients of magnetic fields attract objects. Great, so magnetic fields affect the motion of charges. Moving charges also generate magnetic fields in a way that involves velocity:

$\displaystyle \mathbf{B} = \frac{\mu_0 q}{4\pi r^2} \mathbf{v} \times \mathbf{\hat r}$

This is nice because it too involves a cross product. If B fields are shoving particles sideways, the moving particles had better produce B fields sideways to their own motion, so that that whole “equal and opposite” thing happens. If you have two particles, moving and producing their own magnetic fields, and having those fields shove each other around, they will in fact end up obeying Newton’s laws.

So of the two possible comic book paradigms, young Magneto’s Comic Book Paradigm 2 is more plausible. He pulls on the gate, the gate pulls on him. He applies a few thousand metric tons of force to a submarine, the submarine applies a few thousand metric tons of force to him and he ends up splatted against it. That would make a less entertaining film though.

Can we make up some technobabble to rescue things? Sure, why not. I propose that Magneto is also applying the appropriate force to the iron in the earth’s core to counterbalance whatever he’s doing on the surface. He’ll probably have trouble keeping track of all the torques and I’m not sure if iron at those temperatures and pressures responds to magnetic fields in a useful way anyway, but it’s a start.

What’s that? It’s a comic book and they don’t have to worry about physics in the first place? Preposterous.

1. #1 Dunc
September 24, 2012

Or he could be anchoring himself against the Earth’s magnetic field somehow… Or perhaps he doesn’t even produce the forces himself – maybe he just manipulates the Earth’s magnetic field to do the work?

As for having trouble keeping track of the torques… If you had to actually do the math needed to walk without falling over, you’d never manage it.

2. #2 rpenner
September 25, 2012

“Magnetoâ€™s Comic Book Paradigm 2 is more plausible”

3. #3 Cris
Toronto
September 26, 2012

Magneto’s Magnetic power bothers you more then wolverines ability to magically heal anything Including his own brain…. ??

4. #4 Ouroborus
September 27, 2012

The article make the assumption that Magneto emanates a field himself in some fashion and that this is really the only field he has control over.

It’s more likely (based on his exhibited abilities) that he has the ability to create and control magnetic lenses. Using these lenses to manipulate natural fields (such the Earth’s as mentioned by another poster) would explain his capabilities.

Although I wonder how he’d fare in interstellar space.