Field in a superconducting torus

1. Sep 23, 2011

x_engineer

A question:-

Is it possible to create a magnetic field inside a perfectly superconducting torus if you did not have any to start with? I am talking about a field that goes all the way around the torus, not one that goes partway and doubles back. I am having trouble visualizing how the field lines pass through the central superconducting post in the evolution of the magnetic field.

Also, what is the highest field one can maintain practically inside a superconducting coil?

2. Sep 23, 2011

Drakkith

Staff Emeritus
3. Sep 25, 2011

Born2bwire

I would say no due to your stipulation that the torus did not have any initial field. A superconducting ring must always keep it's flux constant by virtue of Faraday's Law. That is, the line integral of the electric field around the ring, which must be zero for a superconductor due to it's infinite conductivity when in operation, is equal to the time differential of the trapped flux in the ring. Since the line integral of the electric field is zero, the trapped flux must remain constant while the superconductor is operating.

We can imagine a torus to be a continuum of superconducting rings. Since you state that there is no initial field when we turn on the superconductors then there must continue to be zero flux through the torus when in operation.

Now one that doubles back, I could see that arising because then you could have a field where the net flux is still zero (since the field goes in and out of each ring). How one would excite such a field AFTER the torus has been activated I know not, but I can see that it could be physically possible to support such a field.

4. Sep 26, 2011

x_engineer

Drakith: Yes, I am talking about the toroidal field in that diagram.

Born2bwire: What happens if the toroidal sheet is a superconducting coil instead? As you attempt to increase the field does the flux work its way around the spiral gap, and does that effect place limits on how fast you can increase the magnetic field? Would a poloidal coil very close to the toroidal coil therefore be able to detect the change in the toroidal field?

I suppose in a Type II superconductor the presence of a voltage on the coil would allow the flux to directly cross the superconducting wires and enter the toroidal space, and a poloidal coil would not detect any change in the toroidal field. Is that true?