Will it ever stop?

A vertical conducting rod of mass \(m\) and length \(L\) is free to slide on two smooth horizontal conducting rails as shown, where there is a magnetic field of intensity \(B\) directed inside the screen and the resistance of the resistor is \(R\). The rod is given an initial velocity of \(v_0\). Find the total distance travelled by the rod.

Assume that no other forces other than the magnetic force are acting on the rod.


Inspiration and credits for the image.

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