A wire loop carrying current i is placed in the x - y plane as shown in the figure. If an external uniform magnetic field B → = B i ^ is switched on, then the torque acting on the loop is

Step-by-step solution

∵ Magnetic dipole moment of current loop is M → = I A → here area of loop A = Area of sector of circle - area of ∆ 1 3 π a 2 - 1 2 a cos 60 ° × a sin 60 ° × 2 A = π a 2 × 1 3 - 2 × 1 2 × a 2 3 2 a . = π a 2 3 - 3 4 a 2 , A → = π 3 - 3 4 a 2 k ^ ∵ torque on loop placed in uniform magnetic field is τ → = M → × B → = I A → × B → = I π 3 - 3 4 a 2 k ^ × B i ^ = IB a 2 π 3 - 3 4 j ^