Question

If the number of turns and length of the long solenoid are doubled without changing the area, then its self-inductance $L$ will be:

• A. same
• B. 2 times
• C. 3 times
• D. 4 times

Answer 1

The correct option is B 2 times

$N$=total number of turns in solenoid

$l$=length of solenoid

$R$=radius of cross section of solenoid

Magnetic field inside solenoid =$B={\mu }_o\frac{N}{l}i$ where, $\frac{N}{l}$=number of turns per unit length

Now, emf induced= $E=NBA$

$⟹E=N\times {\mu }_o\frac{N}{l}i\times \pi R^2$

$⟹E=\frac{{\mu }_o{N}^2\pi R^2}{l}i=Li$

where $L$=self inductance

Thus, $L=\frac{{\mu }_o{N}^2\pi R^2}{l}$

$⟹L\propto \frac{N^2}{l}$

Hence, on doubling both $N$ and $l$,

$L$ becomes twice.

Answer-(B)