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Force Between Parallel Wires

F=μ0I1I2ℓ2πdF = \frac{\mu_0 I_1 I_2 \ell}{2\pi d}

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Constant used — built into this formula, no need to enter
μ0=0.00000125663706127 N/A2 (H/m)\mu_{0} = 0.00000125663706127\ \text{N/A}^{2}\text{ (H/m)}Vacuum magnetic permeability

Learning zone

Each wire sits in the magnetic field of the other, so they push on each other: parallel currents attract, antiparallel repel. The effect is feeble at bench scale — two wires 1 cm apart carrying 10 A feel just 2 mN per meter — but from 1948 to 2019 it literally defined the ampere. It still matters at scale: adjacent turns in a transformer slam together during a short circuit, and busbars in switchgear must be braced against fault currents that can bend steel.

Force Between Parallel Wires
F=μ0I1I2ℓ2πdF = \frac{\mu_0 I_1 I_2 \ell}{2\pi d}
Where
  • FF= Force
  • I1I_1= Current 1
  • I2I_2= Current 2
  • ℓ\ell= Wire length
  • dd= Separation
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