Question

A toroidal solenoid with an air core has an average radius of $15cm,$ area of cross-section $12c{m}^2$ and $1200$ turns. Ignoring the field variation across the cross-section of the toroid, the self-inductance of the toroid is

• A. 4.6 mH
• B. 6.9 mH
• C. 2.3 mH
• D. 9.2 mH

Answer 1

Answer: (C)

For a solenoid
$B={\mu }_{0}nI$
where $n=\frac{N}{2\pi r}$
$\Rightarrow B=\frac{{\mu }_{0}NI}{2\pi r}$
Flux linked with the solenoid is
$\varphi =NBA$
$\Rightarrow \varphi =\frac{{\mu }_0{N}^{2}A}{2\pi r}$
$\Rightarrow L=\frac{\varphi }{I}=\frac{{\mu }_0{N}^{2}A}{2\pi r}$
$\Rightarrow L=2.3\times 10^{-3}H$