A straight horizontal conducting wire of uniform mass per unit length carries a current I . Another infinitely long straight wire is kept fixed at a distance d directly below it. The upper wire is free to move vertically. For the upper wire to just levitate and remain stationary, what must be the magnitude and direction of the current in the lower wire? [ g is the acceleration due to gravity and ₀ is the permeability

Step-by-step solution

For the upper wire to levitate, the net vertical force on it must be zero. This means the downward gravitational force must be balanced by an upward magnetic force. Since the lower wire is fixed below the upper wire, the magnetic force exerted by the lower wire on the upper wire must be repulsive (pushing it upwards). Two parallel current-carrying wires repel each other when their currents are in opposite directions. Therefore, the current in the lower wire must be in the opposite direction to I . The downward grav