A metal wire of mass m slides without friction on two horizontal rails spaced a distance d apart, as shown in the figure. The track lies in a vertical uniform magnetic field, . A constant current, , flows from generator G along one rail, across the wire, and back down the other rail. We have to find the velocity (speed and direction) of the wire as a function of time, assuming it to be at rest at

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We fix a coordinate system as shown in the figure. In this coordinate system the magnetic field is

The direction of the current flowing through the sliding wire is . Force on the current carrying sliding wire of length d in magnetic field will be

Therefore, force on the sliding wire will be

Mass of the wire is m. It slides without friction on the horizontal rails. As calculated above, it experiences a force of magnitude acting in the direction.

It therefore moves with constant acceleration

in direction. If we use the initial condition that at the sliding wire was at rest, its velocity as a function of time will be given by the function