In a moving coil galvanometer, torque on the coil can be experessed as `tau = ki`, where `i` is current through the wire and `k` is constant . The rectangular coil of the galvanometer having number of turns `N` , area `A` and moment of interia `I` is placed in magnetic field `B`. Find
(a) `k` in terms of given parameters `N,I,A andB`
(b) the torsion constant of the spring , if a current `i_(0)` produces a deflection of `(pi)//(2)` in the coil .
(c) the maximum angle through which the coil is deflected, if charge `Q` is passed through the coil almost instaneously. ( ignore the daming in mechinal oscillations).

Answer

(i)`K=NAB` (ii)`(2NABI_(0))/pi` (iii)`(NABQ)/sqrt(IC)`

Explanation

(i)Torque in coil`=NiAB` (assuming) , `:.K=NAB`
from `NiAB=Ctheta` where C= torsional constant of spring.
`:.C=(NI_(0)AB)/(pi//2)=(2NABI_(0))/pi`
(iii)Angular impulse=change in angular momentum
`inttaudt=DeltaL` or `intBiNA dt=lomega-0`
`:.omega=(BNAQ)/I [:'int "idt"=theta]`
This `omega` is initial angular speed for further motion
Now, by energy conservation [Note:after this it can be solved by using equation`-Ctheta=[(iomegadomega)/(domega)]`
`1/2Iomega^(2)=1/2Ctheta^(2) :.1/2I((BNAQ)/I)^(2)=1/2C theta^(2) :.theta=(NABQ)/sqrt(IC)`