The coil in a moving coil galvanometer experi | vedclass

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(B) For a steady current $i$,the torque $	au = NiAB$ is balanced by the restoring torque $	au_r = C	heta$. Given $	heta = 90^o = \pi/2$ radians,we

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$q\sqrt {\frac{\pi NAB}{2iI}}$

Vedclass · Answer

(B) For a steady current $i$,the torque $	au = NiAB$ is balanced by the restoring torque $	au_r = C	heta$. Given $	heta = 90^o = \pi/2$ radians,we have $NiAB = C(\pi/2)$,which gives the torsional constant $C = \frac{2NiAB}{\pi}$.When a charge $q$ is passed suddenly,the impulse of the torque provides angular momentum to the coil: $\int 	au dt = \int NiAB dt = NABq = I\omega$,where $\omega$ is the initial angular velocity.The kinetic energy $\frac{1}{2}I\omega^2$ is converted into potential energy $\frac{1}{2}C	heta_{max}^2$ at maximum deflection $	heta_{max}$.Substituting $\omega = \frac{NABq}{I}$ and $C = \frac{2NiAB}{\pi}$:$\frac{1}{2}I(\frac{NABq}{I})^2 = \frac{1}{2}(\frac{2NiAB}{\pi})	heta_{max}^2$$\frac{(NABq)^2}{I} = \frac{2NiAB}{\pi}	heta_{max}^2$$	heta_{max}^2 = \frac{(NABq)^2 \pi}{2NiABI} = \frac{q^2 NAB \pi}{2iI}$$	heta_{max} = q\sqrt{\frac{\pi NAB}{2iI}}$.

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