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Electricity & Magnetism
Electricity & Magnetism

Magnetic Field (Long Wire)

B=μ0I2πrB = \frac{\mu_0 I}{2\pi r}

Magnetic field around long straight wire.

Variables

B
Magnetic field
Field strength
In SI units: kg/(A·s²)
T
μ₀
Permeability
4π×10⁻⁷
In SI units: kg·m/(A²·s²)
Allowed values: greater than 0
H/m
I
Current
Current in wire
A
r
Distance
From wire
Allowed values: greater than 0
m

Derivation

From Biot-Savart law or Ampere's law.

Your notes

0/5000

Constants in this formula

μ₀
Vacuum Permeability
1.257 × 10⁻⁶. Measured (CODATA 2018).
H/m

Check value

Round inputs run through this page's calculator, with each constant at its tabulated value. Use it to test your own working or a rearranged form. It is a test case, not a real-world example.

  • μ₀ = 1.257 × 10⁻⁶ H/m (Permeability)
  • I = 2 A (Current)
  • r = 3 m (Distance)

Result: B = 1.333718 × 10⁻⁷ T

Other electricity & magnetism formulas with the same quantities

Where this formula is listed

Common questions

What is the Magnetic Field (Long Wire) formula?

Magnetic Field (Long Wire) is written B = μ₀I/(2πr). Magnetic field around long straight wire. It belongs to Electricity & Magnetism, under Magnetism.

What are the units in B = μ₀I/(2πr)?

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

How is the Magnetic Field (Long Wire) formula derived?

From Biot-Savart law or Ampere's law. The result is B = μ₀I/(2πr).