An infinitely long conductor as shown in figure, carrying a current I with a semicircular loop on X-Y plane and two straight parts, one parallel to X-axis and another coinciding with Z-axis. What is the magnetic field induction at the centre C of the semi-circular loop.

Explanation

The magnetic field at P due to the straight part of conductor parallel to x-axis is
`vec(B_(1)) = (mu_(0))/(4 pi) (i)/((d//2)) hat(k)` ….(1)
The magnetic field at the point P due to the semicircular loo on x-y plane is given by
`vec(B_(2)) = (mu_(0))/(4pi). (pi)/((d//2)) (+ hat(k))` .....(2)
The magnetic field at P due to the straight part coinciding with z-axis is given by,
`vec(B_(2)) = (mu_(0))/(4 pi) . (i)/((d//2)) (-hat(i))` ...(3)
`:.` The total magnetic field at P is given by
`vec(B) = vec(B_(1)) + vec(B_(2)) +vec(B_(3)) = (mu_(0))/(4 pi). (2i)/(d) (1 + pi) hat(k) - (mu_(0))/(4 pi) . (2i)/(d) hat(i) = (mu_(0))/(4 pi) . (2i)/(d) [(1 + pi) hat(k) - hat(i)]`