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)/(4pi R) theta)`, due to arc of radius 4R
`B_(2) = (mu_(0)i)/(4pi (2R)) (pi)`, due to arc of radius 2R
`B_(3) = (mu_(0)i)/(4piR) ((pi)/(2))`, due to arc of radius R
As the current is anticlockwise in all three arcs, therefore, all the fields are prependicular to plane and outwards.
`rArr B_("net") = B_(1) + B_(2) + B_(3)`
`:. B_("net") = (mu_(0)i)/(R) [(1)/(32) + (1)/(8) + (1)/(8)]`
`= (9mu_(0)i)/(32R)`