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A magnetic fluid changes its surface shape in the magnetic field of a current-carrying wire while the current is changing. In the present paper, we propose to study a magnetic fluid bridge which can open or close the channel formed by two cones and a cylinder by imposing the magnetic field of a wire. Numerical modelling of the bridge behavior for different values of magnetic fluid volumes and currents in the wire is done for two cases: when the magnetic fluid wets and does not wet surrounding solid boundaries. It is shown that the presence of limiting cones allows the magnetic fluid to sustain the pressure drop which is much bigger in case of non-wetting than in case of wetting. In case of wetting, the magnetic fluid cannot sustain any pressure drop at small currents, but in case of non-wetting, the magnetic fluid can do it even at zero current. It is found that in case of non-wetting, spasmodic and hysteresis phenomena are possible for some values of magnetic fluid volumes and currents in the wire. The use of a magnetic fluid in valves, dispensers and pumps is one of possible actuation methods.