Question

Self inductance of a long solenoid is directly proportional to
($N$ is no. of turns in solenoid)

• A. $N$
• B. $N^2$
• C. $1/N$
• D. $1/N^2$

Answer 1

The correct option is B $N^2$

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

Hence, $L\propto N^2$

Answer-(B)