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Parallel-Wire Magnetic Force per Meter

Relate two positive current magnitudes, wire separation and magnetic force per unit length in the long parallel-wire vacuum model, with inverse controls and SI units.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

Currents of 10 A and 20 A separated by 1 m give approximately 0.00004 N/m of magnetic force per wire length.

Force per wire length = μ₀ I₁ I₂ / (2πd), using the 2022 CODATA central μ₀ = 1.25663706127 ×10⁻⁶ N/A².

Worked example

Enter these known values and leave the other values blank.

First current magnitude
10 A
Second current magnitude
20 A
Wire center-to-center separation
100 cm
Magnetic force per unit wire length
0.00004 N/m

Assumptions and limitations

  • This is a long, straight, parallel-wire approximation in vacuum. Separation is measured between wire axes; finite ends, thick-wire geometry, nearby conductors and magnetic materials are not modeled.
  • The output is force per wire length, in N/m or a selected SI force prefix per meter. Its denominator stays one meter when the separation control uses centimeters, inches or another length unit.
  • Current values and the result are positive magnitudes. Same-direction parallel currents attract; opposite-direction parallel currents repel. This scalar calculator does not supply a vector direction.
  • Both currents, separation and force per length must be positive in this operating model. Zero-current cases cannot uniquely recover an unknown separation or another current and are outside its retained domain.
  • The vacuum permeability is the NIST 2022 CODATA measured central value, with standard uncertainty 0.00000000020 ×10⁻⁶ N/A². It is not an exact SI defining constant; numerical results do not establish greater physical precision than the model or inputs.

Common questions

Does this calculate the total force on a finite wire?

The result is force per wire length. Multiplying by a length gives a total-force approximation only when the long-wire assumptions hold throughout that segment.

Why does changing separation to feet not change the per-meter force denominator?

Separation is converted internally to meters. The output selector independently uses N/m and its SI prefixes.

References

Require positive second-current and force-per-length magnitudes instead of the captured bare truthy predicates, and declare all five output units as force per meter while preserving numeric conversions. Use the NIST 2022 CODATA measured vacuum-permeability coefficient in the complete forward/inverse graph, guarding all four denominators while retaining positive current and separation domains.

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