We have studied the force in mesoscopic wires in the presence of an external magnetic field along the wire using a free electron model. We show that the applied magnetic field can be used to affect the force in the wire. The magnetic field breaks the degeneracy of the eigenenergies of the conduction modes, resulting in more structure in the force as a function of wire length. The use of an external magnetic field is an equilibrium method of controlling the number of transporting channels. Under the least favorable circumstances (on the middle of a low conduction step) one needs about 1.3 T to see an abrupt change in the force at fixed wire length for a mesoscopic bismuth wire.

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