Field of a Straight Wire

This formula gives the magnetic field strength at a distance r from a very long, straight wire carrying current I. It comes from Ampère’s law and the circular symmetry around the wire: the field lines form concentric circles, so the field is the same everywhere on a circle of radius r and falls off as 1/r. The constant μ0 sets the scale of magnetic effects in vacuum, and the direction of the field is tangential to those circles, given by the right-hand rule.

Use it for idealized long straight conductors when you want the magnetic field at a point outside the wire, especially in electrostatics/electromagnetism problems or circuit analysis. It is appropriate when the wire length is much larger than the distance r and edge effects from the ends can be ignored.

• Using the formula for a finite wire or a wire near its ends, where the long-wire approximation is not valid
• Forgetting to convert the distance r into metres before calculating
• Confusing magnetic field magnitude with direction; the field circles the wire and is not along the wire