Ampere's Law

\oint \vec{B} \cdot d\vec{l} = \mu_0 I_{enc}

Line integral of magnetic field around closed loop equals μ₀ times enclosed current.

Variables

∮B·dl

Line integral

Around closed path

In SI units: kg·m/(A·s²)

T·m

μ₀

Permeability

4π×10⁻⁷

In SI units: kg·m/(A²·s²)

H/m

I_enc

Enclosed current

Current through loop

Derivation

One of Maxwell's equations (magnetostatics form).

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

Biot-Savart Law (Magnetism) shares Permeability
Energy Density (Magnetic Field) (Magnetism) shares Permeability

Where this formula is listed

Electricity & Magnetism formulas, under Magnetism, alongside Magnetic Force on Charge, Magnetic Force on Wire, Cyclotron Frequency, Cyclotron Radius and Hall Voltage.
In the electricity & magnetism list it comes after Hall Voltage and before Faraday's Law.
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 Ampere's Law formula?

Ampere's Law is written ∮B⃗ · dl⃗ = μ₀I_enc. Line integral of magnetic field around closed loop equals μ₀ times enclosed current. It belongs to Electricity & Magnetism, under Magnetism.

What are the units in ∮B⃗ · dl⃗ = μ₀I_enc?

In SI units, ∮B·dl is line integral, measured in kg·m/(A·s²); μ₀ is permeability, measured in kg·m/(A²·s²); I_e nc is enclosed current, measured in A.

How is the Ampere's Law formula derived?

One of Maxwell's equations (magnetostatics form). The result is ∮B⃗ · dl⃗ = μ₀I_enc.