Figure shows a small loop carrying a current I. The curved portion is an arc of a circle of radius R and the straight portion is a chord to the same circle subtending an angle `theta`.The magnetic induction at centre O is

Options

A. zero
B. always inward irrespective of the value of `theta`
C. inward as long as `theta` is less than `pi`
D. always outward irrespective of the value of `theta`

Answer

C

Explanation

The magnetic field due to finite wire at the centre of the loop will be
`B_(1)=(mu_(0)I)/(4piR(cos theta))(sin theta+sin theta)` (From `=(mu_(0)I)/(2piR)tan theta`
Right hand thumb rule, the magnetic field will be inward)
the magnetic field due to the circular loop will be
`B_(2)=(mu_(0)I)/(4piR)theta` (The magnetic field will be outward direction)
The net magnetic field at the centre is
`B=B_(1)-B_(2)`
`B=(mu_(0)I)/(4piR)(2tantheta-theta)`
For `thetagepi,2tan theta-theta lt 0`, therefore magnetic field will be outward for
`thetagepi` and inward for `thetalepi`.