Magnetic Field of a Straight Wire Calculator
Enter current I and distance r to compute the magnetic field B=μ₀I/(2πr). I=10 A, r=0.05 m → B≈4.0×10⁻⁵ T (≈0.4 G).
Input Data
Results
At a glance:Magnetic field of a long straight wire (Biot and Savart, 1820; Ampère, 1826): B=μ₀I/(2πr), where μ₀=4π×10⁻⁷ H/m is the vacuum permeability, I the current, r the perpendicular distance. Direction given by the right-hand rule: thumb along current, fingers curl in the B direction. Physical meaning: a current produces a circular magnetic field around the wire, decaying as 1/r. History: Oersted discovered that a current deflects a compass needle in 1820; Biot-Savart gave the quantitative law; Ampère formulated the circuital law. Classic example: I=10 A, r=5 cm → B=4π×10⁻⁷×10/(2π×0.05)=4.0×10⁻⁵ T≈0.4 G (about the Earth's field). Applications: (1) power-line magnetic-field exposure assessment; (2) electromagnets and solenoids (sum of wires); (3) transformer/motor design; (4) MRT/rail current sensing; (5) magnetic-shielding design.
Formula
B = μ₀·I / (2π·r)
μ₀ = 4π×10⁻⁷ H/m (vacuum permeability)
Direction: right-hand rule (thumb = current, fingers = B)
Turn it around: I = B·2πr / μ₀
Convert: 1 T = 10⁴ G
$$B = \frac{\mu_0 I}{2\pi r}, \quad \mu_0 = 4\pi\times 10^{-7}\ \text{H/m}$$How to Use
- Enter current I (A) and distance r (m).
- The tool computes B=μ₀I/(2πr) (T, G).
- Example: I=10 A, r=0.05 m → B≈4.0e-5 T (≈0.4 G).
Magnetic Field of a Straight Wire at Various Distances
| I (A) | r (m) | B (T) | B (G) |
|---|---|---|---|
| 10 | 0.01 | 2.0e-4 | 2.0 |
| 10 | 0.05 | 4.0e-5 | 0.40 |
| 100 | 0.1 | 2.0e-4 | 2.0 |
| 1000 | 1 | 2.0e-4 | 2.0 |
| 16 | 0.3 | 1.07e-5 | 0.107 |
B=μ₀I/(2πr). B falls as 1/r. At 0.3 m from a 16 A wire B≈0.1 G, comparable to Earth's field. High-voltage lines (thousands of A) need distance to meet exposure limits (ICNIRP ~100 μT public).
Case Studies
Power-Line Magnetic-Field Exposure
A 33 kV distribution line carrying 500 A: at r=1 m B=μ₀×500/(2π×1)=1.0e-4 T=1 G, at r=5 m drops to 0.2 G.
ICNIRP public limit is 100 μT (1 G) at 50 Hz; residential exposure is usually <0.4 G, well within limits.
Hong Kong power cables are mostly underground; at 1 m depth B at street level is already <0.1 G. Shielding uses high-permeability material (mu-metal).
MRT / Rail Current Return Sensing
Hong Kong MTR third-rail current ~1000 A; at 0.5 m B≈4e-4 T=4 G, easily detected by a Hall sensor for train positioning.
The circular field direction reverses with current direction, letting the system distinguish traction vs braking current.
Overhead catenary (KCR) uses similar sensing; noise from adjacent lines is cancelled by differential coils.
FAQ
Why does the magnetic field decay as 1/r?
From Ampère's circuital law ∮B·dl=μ₀I, the circular field at radius r gives B·(2πr)=μ₀I, so B=μ₀I/(2πr). The 1/r dependence is a 2D geometry effect (field lines spread over a circle of circumference 2πr). This differs from a point dipole (1/r³) or infinite sheet (constant). It holds for an infinitely long straight wire; near the ends finite-length corrections apply.
How to determine the direction?
Right-hand rule: point your right thumb in the direction of conventional current (positive to negative), and your fingers curl in the direction of the magnetic field (circulating around the wire). The field is azimuthal (tangent to circles centered on the wire). Reversing the current reverses B. The cross product form is dB=(μ₀/4π)·I·dl×r̂/r².
What is the difference from a solenoid field?
A single straight wire gives B=μ₀I/(2πr) (circular, 1/r). A long solenoid (N turns per length) gives an internal field B=μ₀nI (nearly uniform, independent of r inside). A solenoid is many wires in series whose fields add along the axis, producing a uniform interior field and near-zero exterior field. Transformers and electromagnets use solenoids (or toroids) for strong uniform fields, whereas a single wire gives a weak local field.
Is it dangerous to live near power lines?
Magnetic fields from power lines are non-ionizing and several orders of magnitude below limits at typical residential distances. ICNIRP sets 100 μT (1 G) for public exposure at 50/60 Hz; measured values at property boundaries are usually <0.4 G. Long-term epidemiological studies (e.g. childhood leukemia) show weak associations at very high exposures (>0.3-0.4 μT), but causality is unproven. Underground cabling (as in Hong Kong) further reduces exposure.
How does this relate to the force between wires?
Two parallel wires with currents I₁, I₂, separated by d, each sits in the other's field B=μ₀I/(2πd). The force per unit length is F/L=μ₀I₁I₂/(2πd). Same-direction currents attract, opposite directions repel. This is the basis of the SI ampere definition (historically) and of railguns / coilguns. The 1/r field law directly gives the 1/d force law.
Related Tools
References
Content reviewed by the Calculatorism editorial team. Results are for reference only; please refer to the relevant authorities for the official figures.