Magnetism

In a moving coil galvanometer, torque on the coil can be expressed as \(\tau=k i\), where \(i\) is current through the wire and \(k\) is constant. The rectangular coil of the galvanometer having numbers of turns \(\mathrm{N}\), area \(\mathrm{A}\) and moment of inertia I is placed in magnetic field B. Find

(A) \(k\) in terms of given parameters \(\mathrm{N}, \mathrm{I}, \mathrm{A}\) and B;

(B) The torsional constant of the spring, if a current \(i_{0}\) produces a deflection of \(\frac{\pi}{2}\) in the coil;

(C) The maximum angle through which coil is deflected, if charge \(\mathrm{Q}\) is passed through the coil almost instantaneously. (Ignore the damping in mechanical oscillations.)