Find the magnetic field at the centre O of the loop shown in the figure.

Explanation

Due to straight parts, there is no magnetic field at O. There are three fields at O.
`B_(1)=(mu_(0)i)/(4pi(4R))xx(pi)/2 " "( :. B=(mu_(0)i)/(4piR) theta)`, Due to arc of radius 4R
`B_(2)=(mu_(0)i)/(4pi(2R))(pi)`, due to arc of radius `2R`
As the currenct is anticlockwise in all three arcs, therefore, all the fields are perpendicular to plane and outwards.
`impliesB_("net")=B_(1)+B_(2)+B_(3)`
`:.B_("net")=(mu_(0)i)/R[1/32+1/8+1/8]=(9mu_(0)i)/(32R)`