A long straight wire along the z-axis carries a current I in the negative z direction. The magnetic vector field B→ at a point having coordinates (x, y) in the z = 0 plane is

Magnetic field at Pis B→, perpendicular to OP in the direction shown in figure.So,  B→ = B sin θi^  −  B cos θ j^Here  B= μ02π  Irsin θ  =  yr  and  cos θ = xr∴  B→=μ02π . Ir2  yi^−xj^  =  μ0Iyi^−xj^ 2π x2 + y2                                                 as  r2 =  x2 +  y2