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A current I flows an infinitely long wir...

A current `I` flows an infinitely long wire with cross section in the form of a semi - circular ring of radius `R`. The magnitude of the magnetic induction along its axis is :

A

`(mu_0I)/(pi^2R)`

B

`(mu_0I)/(2pi^2R)`

C

`(mu_0I)/(2piR)`

D

`(mu_0I)/(4piR)`

Text Solution

Verified by Experts

The correct Answer is:
A
`lamda = I/(piR)`
`dB=(mu_0/(4pi))(2I)/R,I=lamdaR"d"theta`
`:. B = int_(-pi//2)^(pi//2)dB cos theta`
`implies (mu_0lamda)/(2pi)int_(-pi//2)^(pi//2)cos theta "d" thetaimplies (mu_0lamda)/(pi)=(mu_0I)/(pi^2R)`
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