A coil having `N` turns is would tightly in the form of a spiral with inner and outer radii a and `b` respectively. When a current `I` passes through the coil, the magnetic field at the centre is.

Options

A. `(mu_(0)NI)/(b-a)`
B. `(mu_(0)NI)/(2pi(b-a))`
C. `(mu_(0)NI)/(2(b-a))"In"b/a`
D. `(mu_(0)NI)/(b-a)"In"b/a`

Answer

C

Explanation

Let dN be the number of turns in width dr.
`dN=N/(b-a)dr`
`dB=(mu_(0)dNi)/(2r)=(mu_(0)Ni)/(2(b-a))(dr)/r`
`B=int_(a)^(b)(mu_(0)Ni)/(2(b-a))(dr)/r=(mu_(0)Ni)/(2(b-a))Inb/a`