A small circular loop of conducting wire has radius  a and carries current  I. It is placed in a uniform magnetic field B perpendicular to its plane such that when rotated slightly about its diameter and simple harmonic motion of time period  T. If the mass of the loop is  m then

τ¯=M¯×B¯The deflecting torque τ¯d=Iα  ,    Restoring torque  τ¯r=-MBsinθAt equilibrium  τ¯d=τ¯rIα=−MBsinθ ​⇒  Iα=−MBθ        for small θ , sinθ≃  θ​⇒  α=−MBIθ    ​⇒  ω=MBI         ∴T=2πω=2πIMB We know, M=nIA (Magnetic moment)⇒M=1×I×πR2    ​and Moment of Inertia = I=mR22    ​Thus, T=2πmR22I.πR2B        =4π2.mR22.I.πR2B  =2πmIB