Biot–Savart law

Statement

dB = (μ₀/4π) · I·dℓ × r̂ / r² — a current element I·dℓ produces at distance r a field dB perpendicular to the plane of dℓ and r, falling as 1/r².

Why is it true?

This is "Coulomb's law for the magnetic field of currents". For an infinite straight wire carrying I, integrating Biot–Savart yields the familiar B = μ₀I/(2πR) — the field forms concentric circles around the conductor.

For a current loop, the field at the center is B = μ₀I/(2R) — the basis of electromagnets and electric motors.

Applications

Electromagnets and solenoids, electric motors, MRI (superconducting magnets), dynamic loudspeakers, high-voltage power-line field models.

Topics that use this theorem

Related theorems

Step-by-step proofs