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

Question

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

Infinity Learn · Accepted Answer

τ¯$$=M$$¯×B¯The deflecting torque τ¯$$d=I$$α  ,    Restoring torque  τ¯$$r=-MBsin$$θAt equilibrium  τ¯$$d=$$τ¯rIα$$=$$−MBsinθ ​⇒  Iα$$=$$−MBθ        for small θ , $$sin$$θ≃  θ​⇒  α$$=$$−MBIθ    ​⇒  ω$$=MBI$$         ∴$$T=2$$πω$$=2$$$$π$$IMB We know, $$M=nIA$$ (Magnetic$$ $$moment)⇒$$M=1$$×I×π$$R2$$    ​and Moment of Inertia $$=$$ $$I=mR22$$    ​Thus, $$T=2$$$$π$$$$mR22I$$.π$$R2B$$        $$=4$$$$π$$$$2$$.$$mR22$$.I.π$$R2B$$  $$=2$$$$π$$mIB

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

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