A metal rod of mass 200 g and length 1 m falls vertically while maintaining contact with two vertical parallel conducting rails. The rails are connected at the top by a resistor of 10 . A uniform horizontal magnetic field of 2 T is present perpendicular to the plane of the rails. If the acceleration due to gravity is 10 m s ⁻² , the terminal velocity of the rod is _______ m s ⁻¹ . (Assume the resistance of the rod an

Step-by-step solution

At terminal velocity, the downward gravitational force is balanced by the upward magnetic force on the rod. F_ m = mg The induced motional EMF in the rod is given by: E = B v_ t l The induced current in the circuit is: I = E R = B v_ t l R The magnetic force on the current-carrying rod is: F_ m = I l B = ( B v_ t l R ) l B = B² l² v_ t R Equating the magnetic force to the weight of the rod: B² l² v_ t R = mg v_ t = mgR B² l² Substituting the given values ( m = 0.2 kg , g = 10 m s ⁻² , R = 10 , B = 2 T , l = 1 m ):