Question

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

${\mu }_0$ represents the permeability of free space.

• A. $\frac{{\mu }_0{N}^{2}A}{L}$
• B. $\frac{{\mu }_{0}NA}{L}$
• C. ${\mu }_0{N}^{2}LA$
• D. ${\mu }_{0}NLA$

Answer 1

The correct option is A $\frac{{\mu }_0{N}^{2}A}{L}$

Self-inductance of solenoid is given by,

$L={\mu }_0{n}^2\pi R^{2}L={\mu }_0{\left(\frac{N}{L}\right)}^2\pi R^{2}L=\frac{{\mu }_0{N}^{2}A}{L}$