Equal current I flows in two segments of a circular loop in the direction shown in figure. Radius of loop is R. What is the magnitude of magnetic field induciton at the centre of the loop?

Explanation

Magnetic field induction at O due to current through arc ADB is
`B_1=(mu_0)/(4pi)I/Rtheta`
Its direction is perpendicular to the plane of circular loop and upwards.
Magnetic field induction at O due to current through arc ACB is
`B_2=(mu_0)/(4pi)I/R(2pi-theta)`
Its direction is perpendicular to the plane of circular loop and downwards.
`:.` Net magnetic field induction at O is downwards, perpendicular to plane of loop
`B=B_2-B_1=(mu_0)/(4pi)I/R[(2pi-theta)-theta]=(mu_0)/(4pi)(2I)/(R)(pi-theta)=(mu_0I(pi-theta))/(2piR)`