  When the magnetic sector of hot QCD, 3D SU(N) Yang-Mills theory, is described
as a dilute gas of non-Abelian monopoles in the adjoint representation of the
magnetic group, Wilson loops of N-ality k are known to obey a periodic k(N-k)
law. Lattice simulations have confirmed this prediction to a few percent for
N=4 and 6. We describe in detail how the magnetic flux of the monopoles
produces different area laws for spatial Wilson k-loops. A simple physical
argument is presented, why the predicted and observed Casimir scaling is
allowed in the large-N limit by usual power-counting arguments. The same
scaling is also known to hold in two-loop perturbation theory for the spatial
't Hooft loop, which measures the electric flux. We then present new lattice
data for 3D N=8 k-strings as long as 3`fm' that provide further confirmation.
Finally we suggest new tests in theories with spontaneous breaking and in
SO(4n+2) gauge groups.
