A toroid is wound over a circular core. Radius of each turn is `r` and radius of toroid is `R (gt gt r)`. The coefficient of self-inductance of the toroid is given by

Options

A. `L = (mu_(0)Nr^(2))/(2R)`
B. `L = (mu_(0)Nr)/(2R)`
C. `L = (mu_(0)Nr^(2))/(R )`
D. `L = (mu_(0)N^(2)r^(2))/(2R)`

Answer

D

Explanation

`L = (phi)/(I),phi = NAB`
`N = mu_(0)nI`
where `n = (N)/(2 pi R)`
`:. phi = Npi r^(2) (mu_(0)(N)/(2 piR)I)`
`phi = (mu_(0)N^(2)r^(2)I)/(2R)`
`L = (phi)/(I) = (mu_(0)N^(2)r^(2))/(2R)`