How does electric current create a magnetic field?

Electric current creates a magnetic field because magnetic forces are produced by moving electric charges. When an electric current flows through a conductor, such as a wire, it generates a magnetic field that circles around the wire in a plane perpendicular to the direction of the current.412

The relationship between the current and the resulting magnetic field is described by fundamental physical laws:

• Ampère’s law: This law provides a quantitative relationship between the magnetic field and the electric current that produces it. For a long, straight wire, the strength of the magnetic field $B$ at a distance $r$ from the wire is given by $B={\mu }_{0}I/2\pi r$, where $I$ is the current and ${\mu }_0$ is the magnetic permeability of free space.1
• Biot-Savart law: This law allows for the calculation of the magnetic field produced by any shape of circuit by summing the contributions of small segments of the conductor.2
• Right-hand rule: This rule is used to determine the direction of the magnetic field lines, which circle the wire.13

This phenomenon was famously demonstrated by Hans Christian Ørsted, who observed that a current-carrying wire could deflect a compass needle.4