Magnetic Field (Solenoid)

B = \mu_0 nI

Uniform magnetic field inside ideal solenoid.

Variables

Magnetic field

Field inside solenoid

In SI units: kg/(A·s²)

μ₀

Permeability

4π×10⁻⁷

In SI units: kg·m/(A²·s²)

Allowed values: greater than 0

H/m

Turn density

Turns per unit length

Allowed values: greater than 0

1/m

Current

Current in solenoid

Derivation

From Ampere's law with rectangular path.

Your notes

0/5000

Constants in this formula

μ₀

Vacuum Permeability

1.257 × 10⁻⁶. Measured (CODATA 2018).

H/m

Check value

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μ₀ = 1.257 × 10⁻⁶ H/m (Permeability)
n = 2 1/m (Turn density)
I = 3 A (Current)

Result: B = 7.542 × 10⁻⁶ T

Other electricity & magnetism formulas with the same quantities

Magnetic Force on Wire (Magnetism) shares Magnetic field, Current
Biot-Savart Law (Magnetism) shares Permeability, Current
Energy Density (Magnetic Field) (Magnetism) shares Magnetic field, Permeability
Hall Voltage (Magnetism) shares Magnetic field, Current
Magnetic Force on Charge (Magnetism) shares Magnetic field
Cyclotron Frequency (Magnetism) shares Magnetic field

Where this formula is listed

Electricity & Magnetism formulas, under Magnetism, alongside Cyclotron Radius and Ampere's Law.
In the electricity & magnetism list it comes after Magnetic Field (Long Wire) and before Energy Density (Magnetic Field).
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 Magnetic Field (Solenoid) formula?

Magnetic Field (Solenoid) is written B = μ₀nI. Uniform magnetic field inside ideal solenoid. It belongs to Electricity & Magnetism, under Magnetism.

What are the units in B = μ₀nI?

In SI units, B is magnetic field, measured in kg/(A·s²); μ₀ is permeability, measured in kg·m/(A²·s²); n is turn density, measured in 1/m; I is current, measured in A.

How is the Magnetic Field (Solenoid) formula derived?

From Ampere's law with rectangular path. The result is B = μ₀nI.