Past exam of the mathematics course of the University of Cambridge / 2014 / iii / Paper 54 / 2 / c

At the initially resting instant $K_{ij}=0$, and the cold-fluid assumption removes the pressure stress. Sum the $xx$ and $yy$ components of the magnetized-fluid tensor virial theorem. The magnetic and gravitational traces areSince $I_{\perp }=I_{xx}+I_{yy}$ and $g_z=-{\partial }_z\Phi$, this yields the horizontal virial balance of a cold magnetized fluid:Being at rest sets the instantaneous velocity to zero; it does not assert equilibrium or zero acceleration. The fields throughout space contribute to this stress integral, including their vacuum exterior.