  We derive the form of the magnetic stress tensor in a completely general,
stationary magnetic medium, with an arbitrary magnetization field $\vec M(\vec
r)$ and free current density $\vec j(\vec r)$. We start with the magnetic force
density $\vec f$ acting on a matter element, modelled as a collection of
microscopic magnetic dipoles in addition to the free currents. We show that
there is a unique tensor ${\bf T}$ quadratic in the magnetic flux density $\vec
B(\vec r)$ and the magnetic field $\vec H(\vec r)=\vec B-4\pi\vec M$ whose
divergence is $\nabla\cdot{\bf T}=\vec f$. In the limit $\vec M=0$, the
well-known vacuum magnetic stress tensor is recovered. However, the general
form of the tensor is asymmetric, leading to a divergent angular acceleration
for matter elements of vanishing size. We argue that this is not inconsistent,
because it occurs only if $\vec M$ and $\vec B$ are not parallel, in which case
the macroscopic field does indeed exert a torque on each of the microscopic
dipoles, so this state is only possible if there are material stresses which
keep the dipoles aligned with each other and misaligned with the macroscopic
field. We briefly discuss the consequences for the stability of strongly
magnetized stars.
