Ampère's Law
Definition
The magnetic twin of Gauss's law: the magnetic field looping around a wire depends only on the current threading the loop.
Technical definition
∮B·dl = μ₀I_enc. It gives B = μ₀I/2πr around a long straight wire and is one of Maxwell's equations (with Maxwell's displacement-current addition).
Example
A wire carrying 10 A produces B = (4π×10⁻⁷ × 10)/(2π × 0.05) = 40 μT at 5 cm — comparable to Earth's magnetic field.
Common confusion
Ampère's law yields the field directly only for symmetric currents. Like Gauss's law, it is universally true but only a shortcut when symmetry lets you pull B out of the integral.