MHT CET202611 April 2026Morning ShiftPhysicsElectromagnetic InductionActual
A long rectangular conducting loop of width ' l ' mass ' m ' and resistance ' R ' is placed partly in a perpendicular magnetic field ' B '. With what velocity should it be pushed downwards so that it may continue to fall without any acceleration? ( g = acceleration due to gravity)
Options
- AB^2 l^2 R^2 mg
- BmgR B^2 l^2
- Cmgl B^2 R^2
- DmgR^2 Bl
Correct answer
B. mgR B^2 l^2
Step-by-step solution
When the loop falls with a velocity v , the motional emf induced in the top horizontal segment of the loop is given by: = Bvl The induced current in the loop is: I = R = Bvl R This current experiences an upward magnetic force due to the magnetic field B . The magnitude of this force is: F_m = IlB = ( Bvl R )lB = B^2l^2v R For the loop to fall without any acceleration, the net force on it must be zero. Therefore, the upward magnetic force must balance the downward gravitational force: F_m = mg B^2l^2v R = mg Solving