Question

A moving coil galvanometer experience Torque $=ki$, where $i$ is current
If $N$ coils of area A each and moment of inertia I is kept in magnetic field B.
(a) find $k$ in terms of given parameters,
(b) if for current $i$ deflection is $\frac{\pi }{2}$ , find out torsional constant of spring,
(c) if a charge $Q$ is passed suddenly through the galvanometer find out maximum angle of deflection

Answer 1

(a) $\overrightarrow{\tau }=\overrightarrow{M}\times \overrightarrow{B},M=NiA$

$\tau =ki=BiNA$

$k=BNA$

(b) $\tau =K\Theta =BiNA$ ($K$ is torsional constant)

$K=\frac{2BiNA}{\pi }[\because \Theta =\frac{\pi }{2}]$

(c) $\tau =BiNA$

${\int }_0^t\tau dt={\int }_0^{t}BNAidt$

$I_0=BNAQ$

$I_0=\frac{BANQ}{I}$

$\frac{1}{2}Io{)}^2=\frac{1}{2}K{\Theta }^2$ [At maximum deflection whole K.E. will convert in to potential energy of spring]

$\Theta =\sqrt{\frac{Io{)}^2}{K}}=\frac{BANQ}{I}\sqrt{2BiNAI\pi }$

${\Theta }_{max}=Q\sqrt{BNA\pi 2I}$.