Magnetic dipole and magnetic moment

Question

I don't quite understand the meaning of these terms. My physics book just gives the mathematical definition of magnetic moment as $\mu=Ia$, which means nothing to me. I know it has to do with torque. Also, I don't quite understand what a magnetic dipole is. Is it a loop that experiences torque due to a magnetic field? Can anyone help clarify these terms? Thanks.

Answer 1

The magnetic moment, in general, is an indication of the torque that will be experienced by an object when subjected to a magnetic field. $\mu = I\cdot A$ implies that it scales with the area (of a current loop) and the magnitude of the current. You can easily convince yourself that this is so by drawing a simple rectangular current loop, with an axis of rotation running parallel to two of the wires of the rectangle. If you make the rectangle wider, the force on the wires is the same but the torque increases (arm is greater); if you make the wires longer, the force increases but the arm stays the same. An arbitrary loop can be thought of as made from many small rectangles, with the forces on adjacent rectangles canceling (currents in opposite direction).

A magnetic dipole is an idealized current loop - where area goes to zero and current to infinity so that their product is finite. The closer you approximate this situation, the more the field starts to look like a dipole field - analogous with the field created when you approach a positive and negative charge closer and closer together, with the product of charge and distance (the dipole moment) constant.

Of course no magnetic monopoles (which would be the analog of charge for half of a magnetic dipole) has ever been observed, but that hasn't stopped people from adopting the name because of the similarity with the mathematics of an electrical dipole.

And yes, that also means that the dipole moment can be used to compute the torque.