A constant current i is delivered by a current generator I_g through a circuit featuring smooth rails and a wire ab of length l and mass m capable of sliding on the rails. This system is maintained vertically within a uniform horizontal magnetic field B oriented perpendicular to the plane of the rails, as shown in the figure. The wire is observed to stay in equilibrium. Should the wire ab be replaced by a new wire of

Step-by-step solution

For the initial wire of mass m and length l in equilibrium, the downward gravitational force is balanced by the upward magnetic force. The magnetic force on the current-carrying wire is given by F_m = ilB . At equilibrium: ilB = mg When the wire is replaced by a new wire of double its mass ( 2m ), the gravitational force becomes 2mg . Since the current i , length l , and magnetic field B remain constant, the upward magnetic force remains the same: F_m = ilB = mg The net downward force acting on the new wire is: F_