Two solenoids of the same length and the same cross-sectional area have 400 turns and 250 turns, respectively. The ratio of self-inductance of the two solenoids, respectively, is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 64 : 25
The self-inductance of a solenoid is
\( \displaystyle L = \frac{\mu_0 N^{2} A}{l} \)
For the same length and area, \( L \propto N^{2} \), so
\( \displaystyle \frac{L_1}{L_2} = \left(\frac{N_1}{N_2}\right)^{2} = \left(\frac{400}{250}\right)^{2} = \left(\frac{8}{5}\right)^{2} = \frac{64}{25} \)