Consider an electron moving in the xy plane with a non-uniform but periodic magnetic field along the z^ direction: B(r)=z^B(r), with r being a 2D vector. Its periodicity is specified by B(r+aj)=B(r), with {aj} forming a Bravais lattice with primitive unit cell area A. The magnetic flux enclosed in such a unit cell is pΦ0/q, where Φ0 is the flux quantum and p and q are mutually prime integers. Find the size of the magnetic unit cell, and corresponding magnetic translation operators similar to that of Eq. (12.99).