Two solenoids of equal number of turns having their lengths and radii in the same ratio 1 : 3. The ratio of their self inductances \( L_1 : L_2 \) will be:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 1 : 3
The self inductance of a solenoid of N turns, area of cross-section A and length l is \( L = \mu_0N^{2}A/l \). Here N is the same, so \( L\propto A/l \), and the area is \( A = \pi r^{2}\propto r^{2} \).
\( \displaystyle L\propto\frac{r^{2}}{l} \)
\( \displaystyle \frac{L_1}{L_2} = \left(\frac{r_1}{r_2}\right)^{2}\times\frac{l_2}{l_1} = \left(\frac{1}{3}\right)^{2}\times\frac{3}{1} = \frac{1}{3} \)