2.0000e-4
N
-2.0000e-4
N
2.0000e-4
N/m
-2.0000e-4
N/m
2.0000e-5
T
2.0000e-5
T
2.0000e-4
N
-2.0000e-4
N
2.0000e-4
N/m
-2.0000e-4
N/m
2.0000e-5
T
2.0000e-5
T
The Magnetic Force Between Wires Calculator computes the force between two parallel current-carrying conductors using the formula $$F = \frac{\mu_0 I_1 I_2 L}{2\pi d}$$ where I₁ and I₂ are the currents, L is the wire length, and d is the separation distance.
This interaction is fundamental to electromagnetism — it was historically used to define the ampere. Parallel wires carrying currents in the same direction attract each other, while those carrying currents in opposite directions repel. This force is critical in power line design, bus bar engineering, and electromagnetic compatibility analysis.
Each current-carrying wire produces a magnetic field. Wire 1 creates a field at the location of Wire 2:
$$B_1 = \frac{\mu_0 I_1}{2\pi d}$$
Wire 2, carrying current I₂ through length L in this field, experiences a force:
$$F = B_1 I_2 L = \frac{\mu_0 I_1 I_2 L}{2\pi d}$$
By Newton's third law, Wire 1 experiences an equal and opposite force from Wire 2's field. The force per unit length is:
$$\frac{F}{L} = \frac{\mu_0 I_1 I_2}{2\pi d}$$
Direction of force:
This can be understood by examining the field lines: between same-direction wires, the fields partially cancel (lower pressure), while outside they reinforce (higher pressure), creating a net inward force.
Historically, the force between two wires defined the ampere: when two infinitely long parallel wires 1 m apart each carry 1 A, the force per meter is exactly $$2 \times 10^{-7}\,\text{N/m}$$. This definition was replaced in 2019 by fixing the elementary charge value.
The result shows the total force on the wire segment and the force per unit length. For power lines, even small forces per meter can accumulate over long spans, causing mechanical stress. In bus bars carrying thousands of amps, these forces can be enormous during fault conditions and must be accounted for in structural design. Same-direction currents attract (wires pull together), opposite-direction currents repel (wires push apart).
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Two power lines carrying 200 A each, 0.5 m apart over 100 m, experience about 1.6 mN total attractive force — small but relevant for long spans.
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During a 50 kA fault, bus bars 5 cm apart experience 10 kN/m repulsive force — massive mechanical stress requiring robust bracing.
Each wire's magnetic field exerts a Lorentz force on the charges in the other wire. Using the right-hand rule, Wire 1's field at Wire 2's location combined with Wire 2's current direction gives a force directed toward Wire 1. Between the wires, their fields partially cancel, while outside they add — this field-pressure imbalance pushes the wires together.
Before 2019, the ampere was defined as the current that, when flowing in two infinitely long parallel wires 1 m apart in vacuum, produces a force of exactly $$2 \times 10^{-7}$$ N per meter of length. This definition was replaced by fixing the elementary charge at exactly $$1.602176634 \times 10^{-19}$$ C.
The force per unit length between two parallel wires is $$\frac{F}{L} = \frac{\mu_0 I_1 I_2}{2\pi d}$$, where $$\mu_0 = 4\pi \times 10^{-7}\,\text{T·m/A}$$. This is independent of wire length and depends only on the currents and separation.
For household currents (10–30 A), the force is negligible — about 10⁻⁵ N/m. However, in industrial settings with thousands of amps, especially during short-circuit faults (50–100 kA), the forces can reach thousands of newtons per meter, requiring engineered bracing and supports.
This formula assumes infinitely thin wires. For wires with finite radius, it is accurate when the separation is much larger than the wire radius. At very close spacing (comparable to wire diameter), the current distribution across the cross-section matters, and more complex calculations are needed.
In three-phase systems, the currents in the three conductors are 120° out of phase, so the forces oscillate and partially cancel. However, during fault conditions, all phases may carry enormous fault currents simultaneously, producing peak forces that must be considered in bus bar and switchgear design.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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