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A long insulated copper wire is closely ...

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

A

`(mu_0NI)/(2(b-a)) In (b/a)`

B

`(mu_0NI)/(2(b-a)) In ((b+a)/(b-a))`

C

`(mu_0NI)/(2b) In (b/a)`

D

`(mu_0NI)/(2b) In ((b+a)/(b-a))`

Text Solution

Verified by Experts

The correct Answer is:
A
(a) `B=int(mu_0(dN)I)/(2x)= int_a^b(mu_0(N/(b-a)dx)I)/(2x)=(mu_0NI)/(2(b-a))ln(b/a)`
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