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).

Explanation

(a) The torque acting on the coil of moving coil galvanometre is
`tau=NiAB`
Given `tau=ki`
`ki=NiAB implies k=NBA`
(b) If C is torsional constant of the spring of galvanometre, then
`tau=C theta`
`Ni_0AB=C(pi/2) implies C=(2NBAi_0)/pi`
(c) If `q_m` is the maximum deflection, then from conservation of energy
`1/2C theta^_m^2=1/2Iomega^2 implies theta_m=sqrt(I/C) omega`.....(i)
we have `tau=NiAB` Put `tau=(dL)/(dt)` where `L` is angular momentum.
`(dL)/(dt)=N((dQ)/(dt))AB` or `dL=NABdQ`
Integrating `int_0^LdL=NABint_0^QdQ implies L=NABQ`
If `omega` is angular velocity,
Put `L=Iomega`
`Iomega=NABQ`
`omega=(NABQ)/I....(ii)`
Subtituting this value in Eq. (i), we get
`theta=sqrt(I/C). (NABQ)/I=(NBAQ)/({sqrt((2NABi_0I)/pi)}) =Qsqrt((piNAB)/(2Ii_0))`.