Question

The self-inductance of a solenoid of length $l,$ area of cross-section $A$ and having $N$ turns is

• A. ${\mu }_0{N}^{2}A/l$
• B. ${\mu }_{0}NA/l$
• C. ${\mu }_0{N}^{2}lA$
• D. ${\mu }_{0}NAl$

Answer 1

Answer: (A)

Self-inductance $L={\mu }_0{n}^{2}lA$
where $n=\frac{N}{l}$ (turns per unit length)
$\therefore L=\frac{{\mu }_0{N}^2}{l^2}.lA=\frac{{\mu }_0{N}^{2}A}{l}$