  In the framework of designing laboratory tests of relativistic gravity, we
investigate the gravitational field produced by the magnetic field of a
solenoid. Observing this field might provide a mean of testing whether stresses
gravitate as predicted by Einstein's theory. A previous study of this problem
by Braginsky, Caves and Thorne predicted that the contribution to the
gravitational field resulting from the stresses of the magnetic field and of
the solenoid walls would cancel the gravitational field produced by the
mass-energy of the magnetic field, resulting in a null magnetically-generated
gravitational force outside the solenoid. They claim that this null result,
once proved experimentally, would demonstrate the stress contribution to
gravity. We show that this result is incorrect, as it arises from an incomplete
analysis of the stresses, which neglects the axial stresses in the walls. Once
the stresses are properly evaluated, we find that the gravitational field
outside a long solenoid is in fact independent of Maxwell and material
stresses, and it coincides with the newtonian field produced by the linear mass
distribution equivalent to the density of magnetic energy stored in a unit
length of the solenoid. We argue that the gravity of Maxwell stress can be
directly measured in the vacuum region inside the solenoid, where the newtonian
noise is absent in principle, and the gravity generated by Maxwell stresses is
not screened by the negative gravity of magnetic-induced stresses in the
solenoid walls.
