A square loop E F G H of side a , mass m and total resistance R is falling under gravity in a region of transverse non-uniform magnetic field given by B = B 0 y a , where B 0 is a positive constant and y is the position of side E F of the loop. If at some instant the speed of the loop is v , then the total Lorentz force acting on the loop is

Step-by-step solution

Motional emf in EH and FG = 0 as v → || I → Motional emf in EF is e 1 = B 0 y a a v ⁡ = B 0 y v ⁡ Similarly, motional emf in GH will be e 2 = B 0 y + a a a v ⁡ = B 0 y + a v ⁡ Polarities of e 1 and e 2 are shown in adjoining figures. So the net emf is e = e 2 - e 1 e   =   B 0 av i = e R = B 0 a v ⁡ R F EF = B 0 a v ⁡ R a B 0 y a (downwards) F GH = B 0 a v ⁡ R a B 0 y + a a F GH = B 0 2 a v ⁡ R y + a (upwards) Net Lorentz force on the loop F net