Biot–Savart Law
Definition
The recipe for the magnetic field of any current shape — add up the tiny field contributions of every bit of wire.
Technical definition
dB = (μ₀/4π) I dl × r̂/r². Integrating gives the field of loops, solenoids, and arbitrary wires; it reduces to Ampère's law for symmetric cases.
Example
At the center of a circular loop of radius R carrying current I, Biot–Savart gives B = μ₀I/2R — the formula behind Helmholtz coils.
Common confusion
The Biot–Savart law is not limited to straight wires — handling any shape is its whole point. Ampère's law is the one that demands symmetry.