A circular coil of 16 turns and radius 10 cm carrying a current of 0.75 A rests with its plane normal to an external field of magnitude `5.0xx10^(-2)T`. The coil is free to turn about an axis in its plane perpendicular to the field direction . When the coil is turned slightly and released , it oscillates about its stable equilibrium with a frequency of 2.0 `s^(-1)` . What is the moment of inertia of the coil about its axis of rotation ?

Explanation

`N = 16 , r = 10 cm = 10 xx10^(-2) m, I = 0.75A`
`B = 5.0 xx10^(-2)T, upsilon=2.0s^(-1)`
`T=2pisqrt(I/(mB))" or "upsilon=1/((2pi))sqrt((mB)/I)`
`:.I=(mB)/(4pi^2upsilon^2)=(ANIB)/(4pi^2upsilon^2)=(pir^2xxNIB)/(4pi^2upsilon^2)=((10xx10^(-2))^2xx16xx0.75xx5.0xx10^(-2))/(4xx(22)/(7)xx4)`
`=(10^(-2)xx16xx0.75xx5xx10^(-2)xx7)/(4xx4xx22)=(0.75xx35xx10^(-4))/22=1.2xx10^(-4)kg m^2`