Velocity of a moving conducting bar in a magnetic field

[Linus Pauling]

1. A conducting bar of length l and mass m rests at the left end of the two frictionless rails of length d in the figure. A uniform magnetic field of strength B points upward. In which direction, into or out of the page, will a current through the conducting bar cause the bar to experience a force to the right? Find an expression for the bar's speed as it leaves the rails at the right end. Express your answer in terms of the variables l, I, B, m, and d.

2. F = Il x B



3. By the right hand rule, the current must be flowing "into the page." However, it isn't clear to me how to get the velocity expression. My instinct would be that v is directly proportional to I, B, and d and inversely proportional to l and m.

 

[rl.bhat]

By using the relevant equation you have found the force F. Mass of the bar is given. Find the acceleration.
Initial velocity of the bar is zero. You want to find the final velocity when the bar leaves the rails by displacing through a distance d.
Using kinematic equation find vf.