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Biot–Savart law
Intermediate
Field from a current element.
dB = μ₀Idl×r̂/4πr²The field from a current element: dB = (μ₀/4π) I dl × r̂/r². Integrating gives fields of wires, loops and coils.
Field of a loop at the centre: μ₀I/2R.
Direction: right-hand rule.
In more detail
The Biot-Savart law gives the magnetic field produced by a small current element, dB = (μ0/4π) I dl × r̂ / r². It is the magnetic analogue of Coulomb's law for a current source.
Real-world uses
- Engineers compute fields near current-carrying conductors using Biot-Savart.
- It is the basis for field calculations in electromagnets.
- Physicists calculate the magnetic field from a complicated shaped wire by adding the contribution of each small current element.
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Frequently asked questions
Is it the same as Coulomb's law?
Similar in form, but it uses a cross product because the field is perpendicular to the current element.
Why is it integrated?
Because a current distribution is made of many small elements, whose fields add.
Is the Biot–Savart law the same as Ampere's law?
They are equivalent for steady currents, but Biot–Savart is easier for finding the field of a finite current element.
Related topics in Magnetism & Induction
Torque on a current loop · Moving coil galvanometer · Electric motor · Field of a long straight wire · Field at centre of a loop · Field on axis of a coil