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The leading force balance in a rapidly rotating conducting fluid when inertial and viscous forces are small, while Coriolis force, pressure, buoyancy and Lorentz force density remain significant. The Rossby number and Ekman number measure the omitted inertia and bulk viscosity. Rotation does not balance an arbitrary magnetic torque: impenetrable axisymmetric boundaries impose the Taylor constraint. Magnetic diffusion can remain in the induction equation even when viscosity is neglected in momentum balance.