Force on a Current-Carrying Wire
F = B · I · L · sin(θ)
Quick answer
This calculator solves F = B × I × L × sin(θ) for Force. With Flux Density 0.5 T, Current 2 A, Conductor Length 10 cm, Angle I to B 45 °, the result is 70.71 mN. It solves in 4 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
A wire carrying current in a magnetic field experiences a force equal to the field times the current times the length of conductor in the field, scaled by the sine of the angle between current and field. This is the motor principle: it converts electrical current into mechanical force. The direction is given by the right-hand (or Fleming’s left-hand) rule.
Variables
- F — Force on the conductor (N)
- B — Magnetic flux density (T)
- I — Current (A)
- L — Length of conductor in the field (m)
- θ — Angle between current and field (degrees)
Practical Notes
Force is maximum when the wire is perpendicular to the field (θ = 90°). This force times radius gives motor torque; it is also the loudspeaker drive force on the voice coil.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| F | Force | N | µN, mN, N, kN |
| B | Flux Density | T | G, mT, T |
| I | Current | A | pA, nA, µA, mA, A, kA |
| L | Conductor Length | cm | mm, cm, m, km |
| theta | Angle I to B | ° | ° |
Step by step
- 1. What you know: Flux Density 0.5 T, Current 2 A, Conductor Length 10 cm, Angle I to B 45 °
- 2. The relation: F = B × I × L × sin(θ)
- 3. Substitute: B = 0.5 T, I = 2 A, L = 10 cm, theta = 45 °
- 4. Result: Force = 70.71 mN
Worked examples
Minimum range
Given: Flux Density 10 G, Current 2 mA, Conductor Length 1 mm, Angle I to B 1.5 °
Result: Force = 5.24 × 10⁻⁵ µN
Low range
Given: Flux Density 10 mT, Current 20 mA, Conductor Length 10 mm, Angle I to B 15 °
Result: Force = 0.5176 µN
Typical
Given: Flux Density 0.5 T, Current 2 A, Conductor Length 10 cm, Angle I to B 45 °
Result: Force = 70.71 mN
High range
Given: Flux Density 1.5 T, Current 100 A, Conductor Length 1 m, Angle I to B 75 °
Result: Force = 144.9 N
Maximum range
Given: Flux Density 15 T, Current 1 kA, Conductor Length 10 m, Angle I to B 750 °
Result: Force = 75 kN
Solving for each variable
Solve for Force
Flux Density 10 G, Current 2 mA, Conductor Length 1 mm, Angle I to B 1.5 ° → 5.24 × 10⁻⁵ µN
Solve for Flux Density
Force 1 mN, Current 2 mA, Conductor Length 1 mm, Angle I to B 1.5 ° → 19100 T
Solve for Current
Force 1 mN, Flux Density 10 G, Conductor Length 1 mm, Angle I to B 1.5 ° → 38.2 kA
Solve for Conductor Length
Force 1 mN, Flux Density 10 G, Current 2 mA, Angle I to B 1.5 ° → 19.1 km
How Force changes with Flux Density
| Flux Density (input) | Force (result) |
|---|---|
| 50 mT | 7.071 mN |
| 125 mT | 17.68 mN |
| 0.25 T | 35.36 mN |
| 0.375 T | 53.03 mN |
| 0.5 T | 70.71 mN |
| 0.75 T | 106.1 mN |
| 1 T | 141.4 mN |
| 2 T | 0.2828 N |
| 3.5 T | 0.495 N |
| 5 T | 0.7071 N |
The same result in other units
| Unit | Value |
|---|---|
| µN | 70710 |
| mN | 70.71 |
| N | 0.07071 |
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<p><a href="https://vbatpower.com/formulas/force-on-wire/">Force on a Current-Carrying Wire</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Force on a Current-Carrying Wire?
Use F = B × I × L × sin(θ). With Flux Density 0.5 T, Current 2 A, Conductor Length 10 cm, Angle I to B 45 °, Force works out to 70.71 mN.
What is the formula for Force on a Current-Carrying Wire?
The formula is F = B × I × L × sin(θ). A wire carrying current in a magnetic field experiences a force equal to the field times the current times the length of conductor in the field, scaled by the sine of the angle between current and field.
How do you find Flux Density when you know the other values?
Rearrange for Flux Density: with Force 1 mN, Current 2 mA, Conductor Length 1 mm, Angle I to B 1.5 °, Flux Density is 19100 T.
How do you find Current when you know the other values?
Rearrange for Current: with Force 1 mN, Flux Density 10 G, Conductor Length 1 mm, Angle I to B 1.5 °, Current is 38.2 kA.
What units does Force on a Current-Carrying Wire use?
Force is shown in µN, mN, N. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
Related Concepts
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