A part of a long wire carrying a current `i` is bent into a circle of radius `r` as shown in figure. The net magnetic field at the centre `O` of the circular loop is

Options

A. `(mu_(0)r)/(4r)`
B. `(mu_(0) i)/(2pi r)`
C. `(mu_(0)i)/(2pi r) (pi + 1)`
D. `(mu_(0) i)/(2pi r) (pi - 1)`

Answer

C

Explanation

The given circuit can be considered as follows:

`B_(loop) = (mu_(0) i)/(2r) o.`
`B_("condcutor") = (mu_(0) i)/(2pi r) o.`
`B_("net") = (mu_(0)i)/(2pi r) (pi + 1) o.`