A wire carrying current `I` has the shape as shown in the adjoining figure. Linear parts of the wire are very long and parallel to X-axis while semicicular portion of radius `R` is lying in `Y-Z` plane. Magnetic field at point `O` is

Options

A. `vec(B)=-(mu_(0))/(4pi) I/R(muhatixx2hatk)`
B. `vec(B)=-(mu_(0))/(4pi) I/R(pihati+2hatk)`
C. `vec(B)=(mu_(0))/(4pi) I/R(pihati-2hatk)`
D. `vec(B)=-(mu_(0))/(4pi) I/R(pihati+2hatk)`

Answer

B

Explanation

Magnetic field at `O`:
`vec(B)_(1)=(mu_(0)I)/(4piR)(-hatk)`
`vec(B)_(2)=(mu_(0)I)/(4R)(-hati)`
`vec(B)_(3)=(mu_(0)I)/(4piR)(-hatk)`
`vec(B)_(O)=vec(B)_(1)+vec(B)_(3)+vec(B)_(2)=(mu_(0)I)/(4piR)(-pi hati-2hatk)`