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)" "ki=NiABimpliesk=NAB`
`(b)` The torsin constant is given by
`C=(tau)/(theta)=(NiAB)/(theta)=(2Ni_(0)AB)/(pi)`
`( c)` Angular impulse
`=int pi dt=int NiABdt=NABQ`
`I omega=NABQimpliesomega=(NABQ)/(I)`
Rotational kinetic energy of coil
`=(1)/(2)Iomega^(2)=(N^(2)A^(2)B^(2)theta^(2))/(2I),=(1)/(2)C theta_(max)^(2)=(N^(2)A^(2)B^(2)theta^(2))/(2I)`
`theta_(max)=thetasqrt((NABpi)/(2Ii_(0))`