A thin insulated wire forms a plane spiral of `N=100` tight turns carrying a current `I=8 mA`.The radii of inside and outside turns (figure) are equal to `a=50 mm` and `b=100 mm`.
(a)The magnetic induction at the centre of the spiral is `N muT`.Then find value of `N`.
(b)The magnetic moment of the spiral with a given current is `N mA m^(2)`.Then find value of `N`.

Answer

A, B

Explanation

`dB=(mu_(0)ni)/(2x)`
`=(mu_(0)[N/(b-a)dx)]/(2x)`
`dB=(mu_(0)Ni)/(2(b-a))(dx)/x`
`B=(mu_(0)Ni)/(2(b-a))"In" [b/a]`
`=(4pixx10^(-7)xx100xx8xx10^(-3))/(2(50xx10^(-3)))xx2.303xx0.3010` `=7muT`
`dM=(Ndx)/(b-a)xxipix^(2)`
`M=N/(b-a)ipi[b^(3)-a^(3)]/3`
`=15mA=m^(2)`