A long straight wire along the z-axis carries a current i in the negative z direction. The magnetic vector field $\overline{\mathrm{B}}$ at a point having coordinates (x,y) in the z = 0 plane is

Magnetic Field of a Long Straight Wire

For a long straight wire along the z-axis carrying a current I in the negative z-direction, the magnetic vector field B at a point with coordinates (x, y) in the z = 0 plane is determined by the right-hand rule and the Biot-Savart law.

The magnitude of the magnetic field at a perpendicular distance r = √(x² + y²) from the wire is:

B = μ₀I / (2πr)

The direction of B is tangential to a circle centered on the wire and lying in the z=0 plane. Using the right-hand rule (thumb in the direction of negative z, fingers curl in the direction of the field), the magnetic field at (x, y) points in the direction of yî - xĵ (or equivalently, is perpendicular to the position vector xî + yĵ).

Thus, the magnetic field vector can be written as:

B = μ₀I (yî - xĵ) / (2π(x² + y²))

So, the correct answer is:

B = μ₀I (yî - xĵ) / (2π(x² + y²))

Note: Sometimes, confusion arises in the sign due to different conventions or step-by-step component analysis. However, the standard result—and the one confirmed by multiple sources—is as above, with the field in the direction yî - xĵ, not xî - yĵ (which would be incorrect for current in the negative z-direction).