An infinite uniform current carrying wire is kept along `z`-axis, carrying current `I_(0)` in the direction of the positive `z`-axis. `OABCDEFG` represents a circle (where all the points are equally spaced), whose centre at point (`4m`, `0m`) and radius `4m` as shown in the figure. If `int_(DEF)vecB*dvecl=(mu_(0)I_(0))/(k)` in `S.I.` unit, then the value of `k` is

Options

A. `4`
B. `8`
C. `3`
D. `6`

Explanation

Draw a circle assuming `OF` as radius and `O` as centre
`underset(MDEFM)(oint)vecB*dvecl=int_(M)^(D)vecB*dvecl+int_(DEF)vecB*dvecl+int_(F)^(M)vecB*dvecl=0`
`rArr0+x-mu_(0)I_(0)(45^(@))/(360^(@))=0`
`rArrx=(mu_(0)I_(0))/(8)`