A straight wire of mass m and length l is able to slide on two parallel plastic rails positioned in a horizontal plane with a separation d . The coefficient of friction between the wire and the rails is . If the wire carries a current i , determine the minimum magnetic field that must be present in the space to make the wire slide on the rails.

Step-by-step solution

Since the rails are made of plastic, they are non-conducting. Therefore, the current i must flow through the entire length l of the wire, not just the part between the rails. Let the magnetic field B be applied vertically to the horizontal plane. The magnetic force acting on the current-carrying wire is given by: F_m = i l B The normal reaction force on the wire due to its weight is: N = m g The maximum static frictional force opposing the motion of the wire is: f = N = m g For the wire to just start sliding on the