A conducting bar with mass \( m \) and length \( L \) slides over horizontal rails that are conn...

A conducting bar with mass \( m \) and length \( L \) slides over horizontal rails that are connected to a voltage source. The voltage source maintains a constant current \( I \) in the rails and bar, and a constant, uniform, vertical magnetic field \( \vec{B} \) fills the region between the rails (as shown in figure).
If the bar has mass \( m \), find the distance \( d \) that the bar must move along the rails from rest to attain speed \( v \).
(1) \( \frac{3 v^{2} m}{2 I L B} \)
(2) \( \frac{5 v^{2} m}{2 I L B} \)
(3) \( \frac{v^{2} m}{I L B} \)
(4) \( \frac{v^{2} m}{2 I L B} \)