One toroid has `1.5 xx 10^4` turns and its axis forms a circle of radius 10 cm. Its cross-section has radius 2 cm. Find inductance of this toroidal ring.

Explanation

`N=1.5xx10^4`
`R=2 cm =2xx10^(-2)` m
`A=piR^2 = pi xx 4 xx 10^(-4)m^2`
r=10 cm =0.1 m
The magnetic induction within the toroidal ring.
`B=mu_0 nI`
`B=(mu_0NI)/(2pir)`[where `n=N/(2pir)`] ..(1)
The flux linked with the ring `phi`=NAB
`therefore phi=NA ((mu_0NI)/(2pir))`
`therefore phi=(mu_0N^2IA)/(2pir)`
`therefore` Inductance of the toroidal `L=phi/I`
`therefore L=(mu_0 N^2A)/(2pir)`
`therefore L=(4pixx10^(-7)xx(1.5xx10^4)^2 xx 4pixx10^(-4))/(2pixx0.1)`
`therefore L=56.52xx10^(-2)` H
`therefore` L=0.5652 H `approx` 0.57 H