For starters it is a POV clock so the spinning disk will be vertically oriented rather than horizontally.
What difference does that make?
But I don't understand how to separate coils on two separate toroids would be magnetically coupled anyway.
Did you read the links? I don't mean wind the toroids normally. I mean wrap the windings around the outside, so if you slipped the windings off, they'd be donut shaped, too.
Imagine a ferrite core, long and cylindrical. There are two windings, one on each end, separated by a small distance in the middle. Feed 50kHz AC into one coil, 50kHz AC comes out the other winding. With me so far?
Now imagine that ferrite core is short, fat, and has a hole in the middle. Same thing with the windings, AC in one winding still comes out the other. Imagine a steel shaft passes through the hole in the middle.
Now just split the ferrite between the two windings, leaving a narrow gap. Now when you feed 50kHz AC into one winding, you still get 50kHz AC from the other, but at a lower voltage. You can now fix one of those in place, and the other can spin, with the steel shaft supporting it.
Tada! Two toroids with the windings around the outside edge placed right next to each otehr.
Or imagine these:http://www.dextermag.com/media/catalog/product/cache/1/image/9df78eab33525d08d6e5fb8d27136e95/D/e/Dexter_Magnetics_Pot_Core_16.jpg
With a winding on each half, separated by a short distance, with a steel shaft through the hole supporting one side on bearings.
Here is the entire book from one of the previous links, on Transformer and Inductor Design. A good read.http://coefs.uncc.edu/mnoras/tr_design/