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

Answer

C

Explanation

`B = B_("loop") + B_("wire")`
`= (mu_(0) i)/(2r) + (mu_(0) i)/(2pi r) = (mu_(0) i)/(2r) [ 1 + (1)/(pi) ] = (mu_(0) i)/(2pi r) [pi + 1] odot`