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

`k = NAB , (b) C = (2i_(0)NAB)/(pi) (c ) Q xx sqrt((NABpi)/(2li_(0)))`

Explanation

`tau = NiAB sin theta (theta=90^(@))`
`tau = NAB iimplies K =NAB`
(b) `ctheta =NIAB implies C(pi)/(2) = Ni_(0) AB`
`C =(2NI_(0)AB)/(pi)`
(c ) angular impulse `int taudt =DeltaL`
`int NiABdt =Iomega`
`NAB int idt = Iomega implies NABQ =Iomega`
`omega = (NA.B0)/(I)`
From energy conservation
Loss os `KE` = Gain of `PE`
`(I)/(2) omega^(2) = (1)/(2) Ctheta_(0)^(2) implies theta_(0) = sqrt((I)/(C) omega`
`theta_(0) = sqrt((Ipi)/(2NI_(0)AB)) . (NABQ)/(I) = sqrt((NABpi)/(2Ii_(0))` .