Why does the magnetic field of a straight wire become weaker farther from the wire?

The magnetic field ($B$) produced by a long, straight wire carrying a steady electric current ($I$) is described by the formula:

$$B=\frac{{\mu }_{0}I}{2\pi r}$$

In this equation, ${\mu }_0$ represents the permeability of free space, and $r$ is the perpendicular distance from the wire to the point where the field is being measured.12

Because the distance $r$ appears in the denominator of this expression, the magnitude of the magnetic field is inversely proportional to the distance from the wire. As you move farther away from the wire, the value of $r$ increases, which mathematically results in a decrease in the strength of the magnetic field. This relationship is a fundamental consequence of Ampère’s law and the Biot-Savart law, which govern how electric currents generate magnetic fields in space.1324