The deflection of a moving coil galvanometer is directly proportional to the current flowing through it, expressed as \( I \propto \theta \).
Given:
\( I_1 = 200 \, \mu\text{A} \)
\( \theta_1 = 60^\circ \)
\( \theta_2 = \frac{\pi}{10} \)
Convert \( 60^\circ \) to radians:
\( \theta_1 = 60^\circ = \frac{\pi}{3} \) radians.
Applying the proportionality:
\( \frac{I_2}{I_1} = \frac{\theta_2}{\theta_1} \)
Substitute known values:
\( \frac{I_2}{200 \, \mu\text{A}} = \frac{\frac{\pi}{10}}{\frac{\pi}{3}} \)
Simplify the ratio of angles:
\( \frac{I_2}{200 \, \mu\text{A}} = \frac{3}{10} \)
Calculate \( I_2 \):
\( I_2 = 200 \, \mu\text{A} \cdot \frac{3}{10} = 60 \, \mu\text{A} \)
Final Answer:
\( \boxed{60 \, \mu\text{A}} \)