Question

While keeping area of cross-section of a solenoid same, the number of turns and length of solenoid one both doubled. The self inductance of the coil will be

• A. halved
• B. doubted
• C. $ \frac{1}{4} $ times the original value
• D. unaffected

Answer 1

The Correct Option is B

The magnetic field inside the solenoid $B=\mu_{0} n i $ Flux, $\phi=B n l A=\mu_{0} n^{2} I A i$ where, $A=$ area of cross-section. As, $ L=\frac{\phi}{L}=\mu_{0} n^{2} l A=\frac{\mu_{0} N^{2}}{l} A$ Here, $n=$ number of turns per unit length $=N / l$ When $N$ and $l$ are doubled, then $L'=\mu_{0} \frac{(2 N)^{2}}{2l} A$ $=2 \mu_{0} \frac{N^{2} A}{l}=2 L$