Work of the Ampère force and parallel currents

In a uniform field a conductor of length l carrying current I and perpendicular to the field lines feels the force F = I·B·l, whose direction follows the left-hand rule. If the conductor moves a distance d along the force, the work is A = F·d = I·B·l·d. The product l·d is the area ΔS swept by the conductor and B·ΔS is the magnetic flux ΔΦ it has crossed, hence A = I·ΔΦ. If the conductor makes angle α with the field lines, F = I·B·l·sinα and the work is multiplied by sinα as well. This work is done not at the expense of the field's own energy but at the expense of the source that maintains the current in the circuit: the magnetic force itself (like the Lorentz force) creates no energy. The same principle is used in electric motors, moving-coil meters and electromagnetic locks.