Question

For a toroid N = 500, radius = 40 cm, and area of cross section = 10 cm². Find inductance

• A. 125 $\mu H$
• B. 250 $\mu H$
• C. $0.00248H$
• D. $zero$

Answer 1

Answer: (A)

If we flow a current i, then
B $=\frac{{\mu }_{0}Ni}{2\pi R}$
${\varphi }_{self}=\left(B\times A\right)\times N=\left(\frac{{\mu }_{0}Ni}{2\pi R}\right)A\times N\Rightarrow {\varphi }_{sell}=\left(\frac{{\mu }_0{N}^{2}A}{2\pi R}\right)i$ and ${\varphi }_{self}=$ Li
$L=\frac{{\mu }_0{N}^{2}A}{2\pi R}=\frac{{\mu }_0}{4\pi }\frac{2N^{2}A}{R}\Rightarrow L=\left(10^{-7}\right)\times \frac{2\times {\left(500\right)}^2\times 10\times {\left(10^{-2}\right)}^2}{0.4}=125\mu H$