Question

Why is a magnetic force the result of a cross product? I don't understand how the resulting force can be perpendicular to both the magnetic field and velocity of a charged particle.

Can someone explain what the electric and magnetic fields are doing on an atomic level some how?

Answer 1

It is not intuitive, I agree. I promise you however that the quantum picture of the magnetic force does not simplify or significantly clarify the picture.

I think the best way to develop a comfort level and beginning of an intuition in this space, is to watch and do as many demonstrations and experiments as you can. A very good place to start is with the excellent MIT lectures with Walter Lewin. Magnetism begins here:
http://ocw.mit.edu/courses/physics/8-02-electricity-and-magnetism-spring-2002/video-lectures/lecture-11-magnetic-field-and-lorentz-force/

As Lewin himself freely admits in several of these lectures, "This is highly non-intuitive!", so if you feel that magnetism and its effects are a little baffling, you're in world-class company.

Answer 2

Here is a picture of a beam of electrons moving in a magnetic field. Perhaps another paintbrush with which to use to paint your own mental picture. http://en.wikipedia.org/wiki/File:Cyclotron_motion.jpg

Answer 3

Granted, it doesn't show the actual force.

Answer 4

In fact, I'm heading out now to buy some wiring and other supplies to replicate two of the magnetism demonstrations Lewin does. Can't wait to show it to some of my friends, and the curious, bright kids next door.

Answer 5

Grab some copper pipe and a magnet. Lenz's law always makes for a cool demonstration. Or even better yet, an aluminum block and an MRI. http://www.youtube.com/watch?v=fxC-AEC0ROk

Answer 6

I'm currently in a calculus based physics course now, and we've moved on to electromagnetic waves already, but I'm still stuck back on fully trying to comprehend electricity and magnetism, flux, lenz, biot-savart, inductance, etc... But most of it just seems like I have to just take their word for it and most people seem to give these very hazy answers! Ahhh, thanks for trying to help though, it's just so confusing compared to the rest of mechanics I've learned in the past.

Answer 7

Yes, it's definitely one of the reasons that it's traditionally taught after kinematics. Demonstrations are key, I think. Seeing is believing.

Answer 8

We've done a lot of cool experiments in my class and lab. But in the end, even though I've observed them, it doesn't seem to do a lot in the way of explaining the WHY there must be a magnetic field in the opposite direction to compensate to induce a emf, etc, etc haha

Answer 9

that's a reasonable set of questions.

But that particular question--why Lenz's law is what it is--has a very good answer. What would happen if the induced magnetic field were in the same direction? You would induce more current which would induce more B field and so on, which is a flat out violation of conservation of energy, and would result in a pretty spectacular explosion in short order.

Answer 10

Sure, I agree with that statement completely, but why does it have to induce a magnetic field at all?