Magnetic Dipole Moments, Force, and Torque

[Pingy]

So, I got a 78 on my last physics exam. Thats 2 points away from an A, yay me! lol

Anyway, I lost the most points on the question about magnetic dipole moments, forces, torques.

I'm having trouble visualizing their direction, but I think its because I don't exactly understand how they interact.

What in the hell is a magnetic dipole moment? What could I possibly use it for? Why is it so important?

Physically, what is a torque? I know its a force, but why is it always a cross product? How does it behave because its a cross product? What could I use a torque for? Why is it important?

I know what a force is lol I just have trouble visualizing the magnetic force direction. Could someone help me out?

Any input is appreciated.

[Shadout Mapes]

I just consider the magnetic dipole moment as an easier way to compute torque on a magnetic loop. You could express everything in terms of magnetic forces and compute the moment arm lengths, etc, but defining the magnetic dipole moment makes the equations simpler.

Torque is mostly important because it relates to angular acceleration in a similar way that force relates to linear acceleration. While the direction of the torque vector is just a convention (similar to magnetic field directions), the fact that torque is a cross product between the force and moment vectors is important in finding the magnitude. If you exert a force on a lever at an exactly right angle, the angular acceleration will be greater than if you pull on the lever at any other angle. In a way you can consider the cross product important in torque because torque is for circular motion, which requires a tangential force, and the magnitude of the cross product is determined by the tangential component of the force vector to the radius.