Magnetic dipole moment of toroid

Question: Must every magnetic configuration have a north and south pole?

Answer: Not necessarily. True only if the source of the field has a net non-zero magnetic moment. This is not so for a toroid or even for a straight infinite conductor.

Picture of a current-carrying toroid loop http://hydrogen.physik.uni-wuppertal.de/hyperphysics/hyperphysics/hbase/magnetic/imgmag/tor.gif

I understand that a straight infinite conductor will not experience a torque in a uniform magnetic field. It will only experience a net force based on its orientation. And so it doesn't have a net magnetic moment.

But I'm unable to visualize how a toroid will behave in a uniform external magnetic field. Since the answer to the above question says that a toroid doesn't have a magnetic dipole moment, I can conclude that it doesn't experience a torque. But does it experience a net force? Please explain how a toroid behaves in an external magnetic field at the basic level of each loop of wire.

• First, all known fundamental sources of magnetism are, at first approximation, magnetic dipoles. There are no observation of free magnetic monopoles yet. Second, an infinite wire may not have, strictly speaking, a net magnetic moment, but how is current supposed to flow in an open loop. It is effectively unphysical on that respect. Third, it is unclear what you ask... What is the toroid exactly? Is there a current? – G. Bergeron Dec 20 '16 at 11:43
• @G. Bergeron 1. All sources of magnetism are either magnetic dipoles or magnetic configurations without any poles. The toroid and straight infinite current-carrying conductors are examples of the later. 2. Current can flow through a straight wire which has +ve and -ve charge reservoirs at either end which aren't connected to each other. Isn't that physically possible?(but I get that it can't be infinite). 3. Thank you for notifying me. I've updated the question. – chopstickPiano Dec 21 '16 at 7:53
• First of all, it is completely untrue that all sources of magnetism either come as dipoles or no poles at all (unless the field is zero). The meaning of poles takes its origin in the multipolar expansion and thus requires that the field be asymptotically zero, which is not the case for objects of infinite extent. A naive calculation for vector potential with objects of infinite extension leads to absurd results that depends on the topology of the space. – G. Bergeron Dec 21 '16 at 9:20
• The case of the charge reservoirs leads to what is essentially a dipole antenna and while it's true it may not have a dipole moment, it will have non-zero higher multipole moments. But now, there will be a net torque from an external magnetic field. For the case of a perfect toroid, even though the external magnetic field is vanishing, there will be multipolar moments of all orders. See en.wikipedia.org/wiki/Toroidal_inductors_and_transformers – G. Bergeron Dec 21 '16 at 9:29