The problem of an arbitrarily conducting porous sphere moving slowly through a current‐carrying, incompressible, and viscous fluid is studied. The effect of permeability on the flow has been studied analytically at low Reynolds number by means of matched asymptotic expansions. The drag force up to order Re is reduced by a factor 1+K/2,Kbeing the permeability associated with the porosity of the sphere. Further, the permeability as well as the current tend to increase the length of eddies behind the porous sphere.