A long insulated copper wire is closely wound as a spiral of `N` turns. The spiral has inner radius a and outer radius `b`. The spiral lies in the `xy`-plane and a steady current I flows through the wire. The`z`-component of the magetic field at the centre of the spiral is

Options

A. `(mu_(0)NI)/(2(b-a))ln(b/a)`
B. `(mu_(0)NI)/(2(b-a))ln((b+a)/(b-a))`
C. `(mu_(0)NI)/((2b))ln(b/a)`
D. `(mu_(0)NI)/((2b))ln((b+a)/(b-a))`

Answer

A

Explanation

`B=int(mu_(o)dNi)/(2x)=int(mu_(0)(N/(b-a)dx)i)/(2x) =(mu_(0)Ni)/(2(b-a))ln(b/a)`