Magnetic Force Between Wires Calculator

Magnetic Force Between Parallel Wires

Two parallel current-carrying wires exert a magnetic force on each other. Wires with currents in the same direction attract; wires with opposite currents repel. This interaction is the basis for the SI definition of the ampere.

Formula

$$\frac{F}{L} = \frac{\mu_0 I_1 I_2}{2\pi d}$$

$F/L$ is the force per unit length in newtons per meter, $I_1$ and $I_2$ are the currents in amperes, $d$ is the separation distance in meters, and $\mu_0 = 4\pi \times 10^{-7}$ T·m/A.

Practical Notes

Same-direction currents produce an attractive force
Opposite-direction currents produce a repulsive force
Force decreases with increasing wire separation

Frequently Asked Questions

Why do parallel currents attract?

Each wire's magnetic field exerts a force on the other wire's moving charges. When currents flow in the same direction, the resulting force is attractive.

How is the ampere defined using wire force?

One ampere is the current that produces a force of 2 × 10⁻⁷ N per meter between two infinitely long parallel wires 1 meter apart in vacuum.

Does wire length matter?

This formula gives force per unit length. Total force equals (F/L) multiplied by the overlapping wire length.

What happens if currents are zero?

No current means no magnetic force between the wires.

How strong is the force at typical currents?

Two 10 A wires 10 cm apart experience about 0.2 mN/m — a small but measurable force used in precision definitions.

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Magnetic Force Between Wires Calculator

Magnetic Force Between Parallel Wires

Formula

Practical Notes

Frequently Asked Questions

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