Dirac spinors are plane wave solutions to the Dirac equation that relies on a background metric (which is actually a Pseudo-Riemannian metric, i.e. not positive definite).
We also know that the plane wave solutions form a basis of a (infinite-dimensional) Hilbert space, which has it's own inner...
Laura,
As far as why the magnitude should be constant inside the hole:
When using ampere's law inside (r<R) a cylindrically symmetric current distribution we have that the magnitude of the magnetic field is proportional to the distance from the axis of the cylinder, r.
When also considering...