system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: Why does the force from a magnetic field on an object act perpendicularly to the direction of the field?

My friends and I in physics tried to look it up but we still just don't understand it.
gpt
I assume you're talking about the Lorentz force? To be perfectly accurate, your question should have been "why is it perpendicular to the field and the direction of motion".

I won't try to answer this in its entirety since it's too much. But let's take a look at a simple example - two parallel wires with currents flowing in them.

I've always found magnetic forces easiest to understand from the standpoint of general relativity. Specifically, length contraction.

Let's say you're in space accelerating towards a planet. As you approach the speed of light, you will see the planet appear to get sucked towards you. The length between yourself and the planet is contracted. Actually, all the lengths along your axis of motion are contracted (including stuff behind you).

Now let's say you have two parallel wires, with currents moving in opposite directions. Imagine yourself as an electron in one of those wires. Now look over to the opposite wire, what do you see? You see electrons moving along your axis of motion. That length is now contracted. Because it's contracted, the density of electrons in the other wire appears to be higher. The wire now has a net charge! There's a net negative charge in the other wire, and you're an electron, so you get pushed away. The wires repel.

Now imagine wires with currents going in the same direction. You're an electron looking over at the opposite wire. You see positive charges moving relative to you! The other wire now appears to be positively charged, so you get sucked towards it! The wires are attracted together.

This is why electric and magnetic fields are two aspects of the same thing - they really ARE the same, just in different reference frames. The parallel wires show the truth - magnetic fields are just relativistic electric fields. Notice that the Lorentz force is always either attractive or repulsive towards the sources, just as an electric field should be.

I hope this helps.