Biot-Savart Law

dB = \frac{\mu_0 I}{4\pi}\frac{dl \sin\theta}{r^2}

Magnetic field from current element.

Variables

Magnetic field

Field from element

In SI units: kg/(A·s²)

μ₀

Permeability

4π×10⁻⁷

In SI units: kg·m/(A²·s²)

H/m

Current

Current in wire

Length element

Small wire segment

Angle

Between dl and r

In SI units: rad

Distance

From element

Derivation

Fundamental law of magnetostatics.

Your notes

0/5000

Constants in this formula

μ₀

Vacuum Permeability

1.257 × 10⁻⁶. Measured (CODATA 2018).

H/m

Other electricity & magnetism formulas with the same quantities

Magnetic Force on Wire (Magnetism) shares Current, Angle
Magnetic Field (Solenoid) (Magnetism) shares Permeability, Current
Magnetic Force on Charge (Magnetism) shares Angle
Energy Density (Magnetic Field) (Magnetism) shares Permeability
Hall Voltage (Magnetism) shares Current
Ampere's Law (Magnetism) shares Permeability

Where this formula is listed

Electricity & Magnetism formulas, under Magnetism, alongside Cyclotron Frequency and Cyclotron Radius.
In the electricity & magnetism list it comes after Magnetic Force on Wire and before Magnetic Field (Long Wire).
Electricity & Magnetism formula sheet, one of 48 formulas printed with symbol keys and SI units.
The full formula index, grouped by category and topic.

Common questions

What is the Biot-Savart Law formula?

Biot-Savart Law is written dB = (μ₀I/(4π))((dl sin θ)/r²). Magnetic field from current element. It belongs to Electricity & Magnetism, under Magnetism.

What are the units in dB = (μ₀I/(4π))((dl sin θ)/r²)?

In SI units, dB is magnetic field, measured in kg/(A·s²); μ₀ is permeability, measured in kg·m/(A²·s²); I is current, measured in A; dl is length element, measured in m; θ is angle, measured in rad; r is distance, measured in m.

How is the Biot-Savart Law formula derived?

Fundamental law of magnetostatics. The result is dB = (μ₀I/(4π))((dl sin θ)/r²).