A square coil of edge ℓ having n turns carries a current i. It is kept on a smooth horizontal plate. A uniform magnetic field B exists in a direction parallel to an edge. The total mass of the coil is M. What should be the minimum value of B for which the coil will start tipping over?

Given-
Number of turns in the coil = n



Edge of the square loop = l



Magnetic field intensity = B



Magnitude of current = i



Angle between area vector and magnetic field, θ = 90°



Torque acting on the coil,


Where


B= applied magnetic field


A= area of rectangular loop


I = current flowing through coil


= angle between the area vector and magnetic field






Torque produced due to weight is


given by,



where m is the mass


g is the acceleration due to gravity


For the coil to start tipping towards downwards,


For minimum value of B,


From (1) and(2)




1