In the shown figure a current 2i is flowing in a straight conductor and entering along the diameter of the circular loop of similar conductor through the point A. The current is leaving the loop along another similar semi-infinite conductor parallel to the plane of the loop through the point D. what is the magnetic field at the centre of the loop P ?

Explanation

The magnetic field at the centre P due to the entering current along diameter is zero.
The magnetic field at P due to the smicircular loop AED is
`vec(B_(1)) = (mu_(0))/(4 pi) . (pi i)/(a)hat(k)` …. (1)
The magnetic field at p due to the semi circular segment AGD is
`vec(B_(2)) = (mu_(0))/(4 pi) . (pi i)/(a) (- hat(k))` .....(2)
and the field at P due to the semi infinite straight conductor is given by
`vec(B_(3)) = (mu_(0))/(4 pi). (2i)/(a) (- hat(k))`......(3)
The net field at P is
`:. vec_(B) = vec(B_(1)) + vec_(B_(2)) + vec(B_(3)) = (mu_(0))/(4 pi). (pi i)/(3) hat(k) - (mu_(0))/(4 pi). (pi i)/(a) hat(k) = - (mu_(0))/(4 pi) . (2i)/(a) hat(k) = (mu_(0))/(2 pi) (i)/(a) (- hat(k))`
The net magnetic field at P is `(mu_(0) i)/(2pi) (1)/(a)` along the perpendicular to the plane of the loop downward