Calculate the torsional constant of the galvanometer if, it has $500\text{turns}$ and each turn has an area $1.0{\text{cm}}^2$. The magnetic field produced by the magnet is $0.02\text{T}$. The deflection in the coil is $0.04\text{radian}$ when a current of $20\text{mA}$ is passed through it.

Given:

Number of turns, $N=500$

Area of each turn, $A=1.0{\text{cm}}^2=1\times {10}^{-4}{\text{m}}^2$

Magnetic field, $B=0.02\text{T}$

Current passing through the coil, $I=20\text{mA}=20\times {10}^{-3}\text{A}$

Deflection in the coil, $\varphi =0.04\text{rad}$

We know that, the torsional constant of a wire used in a moving coil galvanometer is,

$C=\frac{NIBA}{\varphi }$

Substituting the values,

$C=\frac{\left(500\right)\times (20\times {10}^{-3})\times \left(0.02\right)\times (2\times {10}^{-4})}{0.04}$

$=1\times {10}^{-3}\text{Nm/rad}$

Hence, option $\left(C\right)$ is the correct answer.