Acircular coil of 16 turns and radius 10 cm carrying a current of0.75 A rests with its plane normal to an external field of magnitude5.0 ×10−2T. The coil is free to turn about an axis in its plane perpendicularto the field direction. When the coil is turned slightly andreleased, it oscillates about its stable equilibrium with a frequencyof 2.0 s−1.What is the moment of inertia of the coil about its axis of rotation?
Acircular coil of 16 turns and radius 10 cm carrying a current of0.75 A rests with its plane normal to an external field of magnitude5.0 ×10−2T. The coil is free to turn about an axis in its plane perpendicularto the field direction. When the coil is turned slightly andreleased, it oscillates about its stable equilibrium with a frequencyof 2.0 s−1.What is the moment of inertia of the coil about its axis of rotation?
Numberof turns in the circular coil, N= 16
Radiusof the coil, r= 10 cm = 0.1 m
Cross-sectionof the coil, A= πr2= π× (0.1)2m2
Currentin the coil, I= 0.75 A
Magneticfield strength, B= 5.0 ×10−2T
Frequencyof oscillations of the coil, v= 2.0 s−1
∴Magneticmoment, M= NIA
=16 × 0.75 × π× (0.1)2
=0.377 J T−1
Where,
I= Moment of inertia of the coil
Hence,the moment of inertia of the coil about its axis of rotation is 
Numberof turns in the circular coil, N= 16
Radiusof the coil, r= 10 cm = 0.1 m
Cross-sectionof the coil, A= πr2= π× (0.1)2m2
Currentin the coil, I= 0.75 A
Magneticfield strength, B= 5.0 ×10−2T
Frequencyof oscillations of the coil, v= 2.0 s−1
∴Magneticmoment, M= NIA
=16 × 0.75 × π× (0.1)2
=0.377 J T−1
Where,
I= Moment of inertia of the coil
Hence,the moment of inertia of the coil about its axis of rotation is
