  A general method for deriving exact expressions for vector potentials
produced by arbitrarily knotted solenoids is presented. It consists of using
simple physics ideas from magnetostatics to evaluate the magnetic field in a
surrogate problem. The latter is obtained by modelling the knot with wire
segments carrying steady currents on a cubical lattice. The expressions for a
31 (trefoil) and a 41 (figure-eight) knot are explicitly worked out. The
results are of some importance in the study of the Aharonov-Bohm effect
generalised to a situation in which charged particles moving through force-free
regions are scattered by fluxes confined to the interior of knotted
impenetrable tubes.
