The development of magnetohydrodynamic flow due to the passage of a uniform electric current past a sphere immersed in an incompressible viscous conducting fluid extending to infinity is considered. The flow field is the response of the fluid to the Lorentz force set up by the electric current and the associated magnetic field. The solution is based on the assumption that the flow field is weak and has a negligible effect on the electromagnetic variables. We also assume that the convection terms in the momentum equation are negligible. The solution, obtained by means of Laplace transforms, is analytic except for the evaluation of an integral which is done numerically. It is shown that the flow field spreads radially from the sphere into the fluid. The rate of development of the flow field increases with the ratio of the conductivity of the sphere to that of the fluid.