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Shown in the figure is a conductor carry...

Shown in the figure is a conductor carrying a current i. the magnetic field at the origin is :

A

`(mu_(0) i)/(4r) ((hat(i))/(pi) + (hat(j))/(2))`

B

`- (mu_(0) i)/(4r) ((hat(i))/(pi) + (hat(k))/(2))`

C

`(mu_(0) i)/(4 r) ((hat(i))/(2) + (hat(i))/(pi))`

D

`(mu_(0) i)/(4r) ((2hat(i))/(pi) + hat(j))`

Text Solution

Verified by Experts

The correct Answer is:
B
`vec(B_(0)) = vec(B_(1)) + vec(B_(2)) + vec(B_(3))`
Where `vec(B_(1)) = (mu_(0) i)/(4 pi r) (- hat(i))`, `B_(2) = (1)/(4) ((mu_(0) i)/(2r)) (-hat(k))`
and `B_(3) = 0` (since the wire 3 passes through the origin)
`implies B_(0) = - (mu_(0) i)/(4 r) ((hat(i))/(pi) + (hat(k))/(2))`
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