A horizontal conducting rod of mass $$m$$ and length $$L$$ is free to slide on two smooth vertical 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 $$v_0$$ upwards. Find the greatest height $$h$$ that it will attain before falling down. Consider the initial position of the rod as $$h=0$$.