Magnetic Force Between Wires Calculator

About the Magnetic Force Between Wires Calculator

Two parallel wires carrying current exert a magnetic force on each other. Currents in the same direction attract, while currents in opposite directions repel. That relationship is described by Ampere's force law and is a standard result in introductory electromagnetism.

This calculator computes force per unit length, total force over a chosen wire length, and the magnetic field each wire produces at the other's location. The distance chart shows the inverse spacing relationship, and the AWG reference table helps connect the numbers to practical wiring examples.

It is useful when you need to estimate electromagnetic loading on conductors rather than just quote the formula.

When This Page Helps

Parallel conductors can produce measurable forces even when the current is not extreme. Showing the force, field strength, and spacing dependence together makes it easier to size supports and understand why fault currents can create mechanical problems as well as electrical ones.

How to Use the Inputs

1. Enter the current in each wire (they can be different).
2. Enter the center-to-center distance between the wires.
3. Enter the wire length over which to calculate total force.
4. Toggle the current direction checkbox to see attractive vs repulsive forces.
5. Review force per unit length, total force, and B-field at each wire.
6. Use the force-vs-distance chart to see how spacing affects the force.

Example Calculation

Tips & Best Practices

• Force scales as the product of currents — doubling one current doubles the force.
• Force decreases as 1/d — doubling the distance halves the force.
• During fault conditions (short circuits), forces can be enormous — design busbar supports accordingly.
• Use the AWG table to relate wire gauge to maximum current capacity.
• For three-phase power systems, forces between conductors partly cancel due to phase relationships.

Historical Significance

The force between current-carrying wires was first demonstrated by André-Marie Ampère in 1820, shortly after Ørsted discovered the connection between electricity and magnetism. Ampère showed that parallel currents attract and antiparallel currents repel — establishing electrodynamics as a quantitative science and earning him the honor of having the unit of current named after him.

Busbar Engineering

In electrical switchgear and power distribution, copper or aluminum busbars carry thousands of amps. The electromagnetic forces between parallel busbars must be calculated for both normal operation and worst-case fault conditions. Peak fault forces can exceed 10 kN/m, requiring substantial insulating spacers, bracing, and structural analysis.

Modern Definition of the Ampere

Since 2019, the SI ampere is defined by fixing the elementary charge e = 1.602176634 × 10⁻¹⁹ C exactly. This replaced the old definition based on the force between two wires, but the force formula remains physically correct and is still used for practical engineering calculations.

Frequently Asked Questions

• Why do parallel currents attract?

  Each wire creates a magnetic field that exerts a Lorentz force on the moving charges in the other wire. By Ampère's right-hand rule, the geometry works out so same-direction currents attract and opposite-direction currents repel.

• How does this relate to the ampere definition?

  The old SI definition (pre-2019) defined the ampere as the current that produces 2 × 10⁻⁷ N/m of force per meter between two infinitely long, parallel wires 1 meter apart. The modern definition uses a fixed value of the elementary charge.

• Is this force significant in real wiring?

  For household currents (15 A), forces are millinewtons per meter — negligible. For industrial busbars carrying thousands of amps, forces can be hundreds of N/m and require robust mechanical support, especially during fault currents.

• What happens during a short circuit?

  Fault currents can be 10–100× normal current, and the force scales as I². A 10× current increase means 100× force — busbar systems must be designed to withstand these brief but enormous mechanical loads.

• Does the wire material affect the force?

  No — the magnetic force depends only on current and geometry, not wire material. However, wire resistance (material-dependent) affects power loss and heating.

• What if the wires are not parallel?

  This formula assumes parallel, infinitely long wires. For non-parallel or finite wires, numerical integration of the Biot-Savart law is required.