Shows a horizontal magnetic field which is uniform above the dotted line and is zero below it. A long, rectangular, conducting loop of width L, mass m and resistance R is placed partly above and partly below the dotted line with the lower edge parallel to it . with what velocity should it be pushed downwards so that it may continue to fall without any acceleration?

Explanation

Let the uniform velocity of fall be v
The emf is indcued across the upper wire and its magnitude is `epsilon = vBl
The current induced in the frame is ` i=(vBl)/(R )` so that, the magnetic force on the upper arm is `F = ilB = (vB^2l^2)/(R )
This force is in the upward direction
As the frame falls uniformly, this force should balance its weight
Thus, `mg=(vB^2 l^2)/(R )` or, `v=(mgR)/(B^2l^2)`