Hong Life CalculatorsUnderstanding the force between parallel wires calculator — concept and principle
This calculator finds the magnetic force between two long, straight, parallel wires carrying currents, the force per metre, the field one wire creates at the other and whether they attract or repel. It is used in electromagnetism courses and for checking forces on bus bars and cables during high currents.
How it is calculated
F ÷ L = μ₀ I₁ I₂ ÷ (2π d)
B at wire 2 = μ₀ I₁ ÷ (2π d)
- μ₀ = 4π × 10⁻⁷ T·m/A; d is the centre-to-centre distance (entered in mm), L the parallel length in metres.
- Same-direction currents attract; opposite currents repel.
The principle
A current produces a magnetic field that circles the wire and weakens as 1/d. The second wire sits in that field, and a current in a magnetic field feels a sideways force F = B I L. Combining the two gives the formula. Both wires feel equal and opposite forces, as Newton's third law requires. This interaction once defined the ampere: two wires 1 m apart, each carrying 1 A, pushed on each other with 2 × 10⁻⁷ N per metre.
Worked example
Default inputs: 100 A in each wire, same direction, 20 mm apart, 2 m long.
- B at wire 2 = 4π × 10⁻⁷ × 100 ÷ (2π × 0.02) = 0.001 T = 1,000 µT.
- Force per metre = 2 × 10⁻⁷ × 100 × 100 ÷ 0.02 = 0.1 N/m.
- Force on each wire = 0.1 × 2 = 0.2 N = 200 mN.
- The currents flow the same way, so the wires attract (are pulled together).
| Centre-to-centre distance (mm) | Force on each wire (N) |
|---|---|
| 5 | 0.8 |
| 10 | 0.4 |
| 15 | 0.2667 |
| 20 | 0.2 |
| 25 | 0.16 |
| 30 | 0.1333 |
| 40 | 0.1 |
How to read the result
Under normal currents the force is small, as here. It grows with the product of the currents, so a fault current 20 times higher gives 400 times the force, which can bend bus bars and whip cables. Halving the distance doubles the force.
Common mistakes
- Using the edge-to-edge gap instead of the centre-to-centre distance.
- Forgetting the mm-to-m conversion.
- Expecting the formula to hold for short conductors or wide flat bars, where the real force is lower.
- Getting the direction backwards. Like currents attract, which is the opposite of the rule for like charges.
Frequently asked questions
Do parallel currents attract or repel?
Currents in the same direction attract; currents in opposite directions repel.
Why does a household cord not jump when switched on?
At a few amperes the force is tiny, and the two conductors' fields mostly cancel outside the cord.
Is the ampere still defined this way?
No. Since 2019 it is defined by fixing the elementary charge, but the force law is unchanged.
Sources: OpenStax, University Physics Volume 2 (2016), section 12.3 "Magnetic Force between Two Parallel Currents"