Take place at the center of the carrousel. Before turning it on, ask the child to take the bar magnet and sit on the horse. The child is your electron and you are the nucleus. You feel the magnetic field due to the spin of the elecrton, in this case the bar magnet. Take the magnetometer to read of a value. This is the first contribution to the hyperfine field.
Now give the child the charged sphere and turn on the carrousel. The child, the electron, is now a moving charged particle, a current, creating a magnetic field. Take again your magnetometer and read of a value. This is the second contribution to the hyperfine field.
The third contribution is too difficult to demonstrate. You can write an “s” on the charged sphere and swallow it but this is the closest you will get to the Fermi term.