As current I flowing through the loop as shown in figure. The magnetic field at the centre O is

Answer

D

Explanation

The angle, subtended by arc DE at O is `(pi)/(2)` and FC at `O= (3pi)/(2)` the effective magnetic field at O is `B= B_(DE) + B_(FC)`

`=(mu_(0)i)/(4pi 3r)xx (pi)/(2) + (mu_(0)i)/(4pi r) xx ((3pi)/(2))`
`=(mu_(0)i)/(8r) [(1)/(3) + 3]`
`=(5mu_(0)i)/(12r)` acting downwards