A conducting rod of mass m and length L slides without friction on two long horizontal rails. A uniform vertical magnetic field fills the region in which the rod is free to move; as shown in the figure. The generator G supplies a constant current i that flows down one rail, across the rod, and back to the generator along the other rail. We have to find the velocity of the rod as a function of time, assuming it to be at rest at .

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The force on a current carrying conductor in a uniform magnetic field is given by the Lorentz force law,

.

is a vector length of the conductor in the direction of the flow of current in it, and is the magnetic field acting on the current carrying conductor. In our problem

and .

The current flowing in the conducting rod through the rails is maintained by the generator at a constant value . Therefore, force on the rod will be

We note that the force on the conducting rod will be along the negative y-axis.

As the mass of the sliding rod is m and that the rod is assumed to slide on the rails without friction, it will move with acceleration

.

We are given the initial condition that the conducting rod starts from rest at . Therefore, the velocity of the rod as a function of time will be

The direction of motion of the rod is away from the generator.