Magnetic moment and magnetic torque of a current loop

[Gavo]

Hi.
I have a question concerning the magnetic momentum of a current loop.
We know that if we have a circular current loop (a solenoid with N=1), there is a magnetic moment (mu) in the center of the loop given by "mu=S I" (I=current, S =surface enclosed by the loop). So, if there is an external magnetic field B, we can have a torque (tau) given by "tau=mu x B".
In order to calculate this, we need to have a magnetic field with its field lines passing through the center of the surface enclosed by the loop.
What happens when we have a magnetic field with lines passing thruogh the surface of current loop, but not in the center? Would it be any torque? I guess these questions are linked to the fact that the magnetic momentum "mu" of a current loop is defined only in the center of the surface enclosed by the loop (or not?).

Thanks to everyone.

 

[chrisbaird]

The magnetic moment is not "defined only in the center of the loop". The magnetic moment is not a field, it is a single entity attached to a single object. We draw it in the center because that is the center of action, but it describes the entire object. Think of the force on gravity on a donut. The force that the donut feels is a single entity describing the entire object. Because it is a single entity, we only draw one vector arrow. You've got to draw the arrow, somewhere, so you draw it attached to the center of mass because that is the center of action. But for a donut, there is no matter at its center, so is there a problem if we draw the force vector acting on a spot with no matter? No, this is not a problem because the force is not a field. It acts on objects, not on single points in space. So the vector drawn attached to the hole in the middle of the donut is understood to represent the total effect of gravity exerting a force on the entire donut, as if its entire mass where contained at a point which is its center of mass.
It is the same with magnetic moment, electric dipole moment, angular momentum, velocity, etc. They are single-entity vectors which only make sense when attached and describing an object (or system of objects).

For the torque law you describe, it's the number of field lines passing through anywhere in the loop that have an effect. That is why mu is dependent on the S, the entire surface area enclosed by the loop.

 

[Gavo]

Ok, thanks a lot, now it's clear.