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A long wire carrying current 'I' is bent...

A long wire carrying current 'I' is bent into the shape as shown in the figure. The net magnetic field intensity at the centre 'O' is

A

`(mu_(0)I)/(4piR)sqrt(1 + pi^(2))`

B

`(mu_(0)I)/(4piR)sqrt(2 + pi^(2))`

C

`(mu_(0)I)/(4piR)sqrt(4 + pi^(2))`

D

`(mu_(0)I)/(4piR)sqrt(9 + pi^(2))`

Text Solution

Verified by Experts

The correct Answer is:
A
The net magnetic field intensity at the centre 'O' is
`vec(B_(0)) = (mu_(0)I)/(4piR) (-hat(k)) + (mu_(0)I)/(4R) (-hat(i))`
`:. B_(0) = (mu_(0)I)/(4piR) sqrt(1 + pi^(2))`
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