Question

A long solenoid with length $l$ and a radius $R$ consists of $N$ turns of wire,Neglecting the end effects, find the self-inductance.

• A. ${\mu }_0{N}^2\pi R^2/l$
• B. ${\mu }_{0}N\pi R^2/l$
• C. ${\mu }_0{N}^2\pi R^{3}l$
• D. ${\mu }_0{N}^3\pi R^{2}l$

Answer 1

The correct option is A ${\mu }_0{N}^2\pi R^2/l$

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

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

Answer-(A)