If a current of 200 μA deflects the coil of moving coil galvanometer through 60°, then the current required to cause deflection through π/10 radians is

The correct option is 60 μA.

For a moving coil galvanometer, the deflection of the coil ($\theta$) is directly proportional to the current ($I$) flowing through it. This relationship is expressed as:

$I\propto \theta$

From this proportionality, we can set up the ratio for two different instances of current and deflection:

$\frac{I_1}{I_2}=\frac{{\theta }_1}{{\theta }_2}$

We are given the following values in the problem:
Initial current, $I_1=200\mathrm{\mu A}$
Initial deflection, ${\theta }_1=60°$
Target deflection, ${\theta }_2=\frac{\pi }{10}\mathrm{radians}$

To compare the two deflections, we convert the initial deflection ${\theta }_1$ from degrees to radians:
Since $180°=\pi \mathrm{radians}$, we have:

${\theta }_1=60°=60\times \frac{\pi }{180}=\frac{\pi }{3}\mathrm{radians}$

Now, substitute the values of $I_1$, ${\theta }_1$, and ${\theta }_2$ into the ratio formula:

$\frac{200}{I_2}=\frac{\pi /3}{\pi /10}$

Simplifying the right-hand side of the equation:

$\frac{200}{I_2}=\frac{10}{3}$

Solve for the required current $I_2$:

$I_2=200\times \frac{3}{10}$

$I_2=20\times 3=60\mathrm{\mu A}$

Thus, the current required to cause a deflection through $\frac{\pi }{10}$ radians is 60 μA.