A thin insulated wire forms a plane spiral of `N=100` turns carrying a current `i=8mA`. The inner and outer radii are equal to `a=5 cm and b=10 cm`. Find the magnetic induction at the centre of the spiral

Explanation

Let `n=n o .` of turns per unit length along the raidal of spiral. Consider a ring of radii`x` and `x+dx`.
No. of turns in the ring `=ndx. n=(N)/((b-a))`
Magnetic field at the centre due to the ring is
`dB=(mu_(0)(ndx)i)/(2x),` so net field
`Bint dB=underset(a)overset(b)int(mu_(0)ni dx)/(2x)=(mu_(0)ni)/(2)underset(a)overset(b)int (dx)/(x)`
or `B=(mu_(0)ni)/(2)ln ``(b)/(a)or B=(mu_(0)Ni)/(2(b-a))ln``(b)/(a)`
`=(4pixx10^(-7)xx100xx8xx10^(-3))/(2(10-5)xx10^(-2))ln``(10)/(5),B=6.9xx10^(-6)T`