If a long horizontal conductor is bent as shown in figure and a current I is passed in it, find the magnitude and direction of magnetic field induction at the centre of circular part.

Explanation

Let `hatn` be the unit vector perpendicular to the plane of paper upwards. Magnetic field induction at O due to current through the entire structure is
`vecB=vecB_(CG)+vecB_(DEF)=(mu_0)/(4pi)(2I)/(r)hatn+(mu_0)/(4pi)(2piI)/(r)(-hatn)`
`=(mu_0I)/(2r)[1/pi-1]hatn=(mu_0I)/(2r)[1/pi-1]upwards`