Question

An air core solenoid has 1000 turns and is one metre long. Its cross – sectional area is $10c{m}^2$. Its self – inductance is

• A. 2.56 mH
• B. 1.92 mH
• C. 1.26 mH
• D. 2.78 mH

Answer 1

The correct option is C

1.26 mH

For solenoid, $B={\mu }_{0}ni={\mu }_0\frac{N}{l}i$
$\varphi =NBA=N\left[{\mu }_0\frac{N}{l}i\right]A={\mu }_0\frac{N^{2}A}{l}i$
Also $\varphi =Li\therefore L=\frac{{\mu }_0{N}^{2}A}{l}$
So $L=4\pi \times {10}^{-7}\times \frac{(1000{)}^2}{1}\times 10\times {10}^{-4}$
=0.0012566H =1.26mH