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A long insulated copper wire is closely ...

A long insulated copper wire is closely wouind as a spiral of 'N' turns . Thw 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 magnetic field at the centre of the spiral is

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))`

Text Solution

Verified by Experts

The correct Answer is:
`A`
Taking an element strip of radius x and width dx
Area of strip `2pixdx`
Number of turns through area `= (N)/(b-a) dx`
`intdB= underset(a)overset(bmu_(0))int(mu_(0)(N)/((b-a))Idx)/(2x) = (mu_(0)NIln"((b)/(a)))/(2(b-a))`
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