Magnetic Field of a Straight Wire
B = µ0 · I / (2π · r)
Quick answer
This calculator solves B = µ₀ × I / (2π × r) for Flux Density. With Current 2 A, Distance 10 mm, the result is 0.4 G. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
A long straight wire carrying current produces a magnetic field that circles the wire and falls off inversely with distance. The field lines form concentric circles whose direction follows the right-hand rule. This is the starting point for analysing the fields of coils, the coupling between adjacent traces, and magnetic interference from current-carrying conductors.
Variables
- B — Magnetic flux density (T)
- I — Current in the wire (A)
- r — Radial distance from the wire (m)
- µ₀ = 4π×10⁻⁷ H/m —
Practical Notes
At 1 cm from a 1 A wire, B ≈ 20 µT—comparable to Earth’s field. This circulating field is why current loops should enclose minimal area to limit radiated emissions.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| B | Flux Density | T | G, mT, T |
| I | Current | A | pA, nA, µA, mA, A, kA |
| r | Distance | mm | mm, cm, m, km |
Step by step
- 1. What you know: Current 2 A, Distance 10 mm
- 2. The relation: B = µ₀ × I / (2π × r)
- 3. Substitute: I = 2 A, r = 10 mm
- 4. Result: Flux Density = 0.4 G
Worked examples
Minimum range
Given: Current 2 mA, Distance 0.1 mm
Result: Flux Density = 0.04 G
Low range
Given: Current 20 mA, Distance 1 mm
Result: Flux Density = 0.04 G
Typical
Given: Current 2 A, Distance 10 mm
Result: Flux Density = 0.4 G
High range
Given: Current 100 A, Distance 10 cm
Result: Flux Density = 2 G
Maximum range
Given: Current 1 kA, Distance 1 m
Result: Flux Density = 2 G
Solving for each variable
Solve for Flux Density
Current 2 mA, Distance 0.1 mm → 0.04 G
Solve for Current
Flux Density 10 G, Distance 0.1 mm → 0.5 A
Solve for Distance
Flux Density 10 G, Current 2 mA → 4 × 10⁻⁴ mm
How Flux Density changes with Current
| Current (input) | Flux Density (result) |
|---|---|
| 0.2 A | 0.04 G |
| 0.5 A | 0.1 G |
| 1 A | 0.2 G |
| 1.5 A | 0.3 G |
| 2 A | 0.4 G |
| 3 A | 0.6 G |
| 4 A | 0.8 G |
| 8 A | 1.6 G |
| 14 A | 2.8 G |
| 20 A | 4 G |
The same result in other units
| Unit | Value |
|---|---|
| G | 0.4 |
| mT | 0.04 |
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<p><a href="https://vbatpower.com/formulas/b-field-straight-wire/">Magnetic Field of a Straight Wire</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Magnetic Field of a Straight Wire?
Use B = µ₀ × I / (2π × r). With Current 2 A, Distance 10 mm, Flux Density works out to 0.4 G.
What is the formula for Magnetic Field of a Straight Wire?
The formula is B = µ₀ × I / (2π × r). A long straight wire carrying current produces a magnetic field that circles the wire and falls off inversely with distance.
How do you find Current when you know the other values?
Rearrange for Current: with Flux Density 10 G, Distance 0.1 mm, Current is 0.5 A.
How do you find Distance when you know the other values?
Rearrange for Distance: with Flux Density 10 G, Current 2 mA, Distance is 4 × 10⁻⁴ mm.
What units does Magnetic Field of a Straight Wire use?
Flux Density is shown in G, mT. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
Related Concepts
All Fields & Electromagnetism formulas →Need more features?
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