[Physics] Magnetic dipole moment of toroid

electric-currentelectromagnetismmagnetic fieldsmagnetic-momenttorque

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
(source: uni-wuppertal.de)

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.

Best Answer

A torus can be a magnetizable object; what you describe, is a solenoid-like winding bent into a toroidal shape. So, the current is circulating through the hole in the torus, on a minor-diameter route. Such current is called 'poloidal'.toroidal and poloidal

That current is a self-shielding magnetic geometry (and toroids with windings to create poloidal current are highly prized as inductors, because they don't accept external interference, nor radiate). And, yes, the fact that no external field is coupled means that there's no net torque or force.

There is another useful property, in that a poloidal wound magnetizable torus can be driven nonlinear due to added external field which saturates the magnetizable material. Such a saturation imbalances the flux in the torus, and creates coupling (which can be used to detect the external field). This is the principle on which flux-gate magnetic field detection is based.

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