The spring force when stretched by x is F = kx The magnetic force experienced by small element dr is dF = Bidr . The torque 'dτ' due to this force is dτ = rdF = (Bir) dr Total torque = τ = ∫ dτ = Bi
l
∫
0
rdr =
Bil2
2
At equilibrium, net torque about the hinge is zero (kx) l sin 30° -