Magnetic Force Between Wires
Two parallel current-carrying wires exert force on each other. Force per length F/L = μ₀I₁I₂/(2πd). Same-direction currents attract; opposite repel. Wire 1's B at wire 2: B = μ₀I₁/(2πd); F = I₂LB.
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F/L = μ₀I₁I₂/(2πd); doubles if either current doubles. 1 A in each wire, 1 m apart: F/L ≈ 2×10⁻⁷ N/m. Ampere definition: F/L = 2×10⁻⁷ N/m when I₁ = I₂ = 1 A, d = 1 m. Opposite currents repel; parallel currents attract.
Ready to run the numbers?
Why: Force between wires defines the ampere (SI base unit). Power transmission, bus bars, and motor windings experience these forces.
How: Wire 1's B at wire 2 is μ₀I₁/(2πd). Lorentz force on wire 2: F = I₂L × B. Same direction: B curls such that wires attract.
Run the calculator when you are ready.
⚡ Power Transmission Lines
High-voltage power lines carrying 1000A at 10m separation
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🔌 Bus Bars in Switchgear
Parallel bus bars in electrical distribution carrying 500A
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🔊 Speaker Voice Coils
Parallel voice coils in speaker drivers with 2A current
Click to use this example
⚙️ Motor Stator Windings
Adjacent windings in electric motor carrying 10A
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🔋 Transformer Windings
Primary and secondary windings with different currents
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🧪 Laboratory Experiment
Classic physics lab demonstration with 5A currents
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Enter Wire Parameters
Wire Properties
Geometry
Configuration
Medium Properties
For educational and informational purposes only. Verify with a qualified professional.
🔬 Physics Facts
The ampere is defined via force between parallel wires: F/L = 2×10⁻⁷ N/m.
— SI brochure
Power lines: 100 A, 0.5 m apart → F/L ~ 4 mN/m per meter.
— Power engineering
Bus bars in switchgear experience significant forces during faults.
— Electrical design
Lorentz force F = I(L × B) is perpendicular to both L and B.
— Electromagnetism
What is Magnetic Force Between Current-Carrying Wires?
The magnetic force between current-carrying wires is a fundamental phenomenon in electromagnetism where two parallel wires carrying electric currents exert forces on each other. This force arises from the interaction between the magnetic field produced by one wire and the current flowing through the other wire, following Ampère's force law.
Force Per Unit Length
The fundamental quantity F/L = μ₀I₁I₂/(2πd) describes the force per meter of wire length, independent of total wire length.
Attraction vs Repulsion
Wires attract when currents flow in the same direction and repel when currents flow in opposite directions.
Practical Applications
Critical for power transmission lines, motor windings, transformer design, and electrical distribution systems.
How Does Magnetic Force Between Wires Work?
Our calculator employs Ampère's force law to determine the magnetic force between parallel current-carrying wires. The system calculates magnetic fields, force per unit length, total force, and determines whether wires attract or repel based on current directions.
🔬 Calculation Process
- Magnetic Field Calculation: Calculate the magnetic field produced by each wire using B = μ₀I/(2πd)
- Force Per Unit Length: Determine F/L = μ₀I₁I₂/(2πd) using both currents and separation distance
- Total Force: Multiply force per unit length by wire length: F = (F/L) × L
- Direction Determination: Apply right-hand rule to determine attraction (same direction) or repulsion (opposite direction)
- Unit Conversions: Convert between N, mN, T, G, μT for practical engineering applications
When to Use Magnetic Force Between Wires Calculator
This calculator is essential for electrical engineers, physicists, and technicians working with current-carrying conductors. It's particularly valuable for power system design, motor development, transformer engineering, and electrical safety analysis.
Power Transmission
Design high-voltage transmission lines with proper spacing to manage magnetic forces between conductors.
Motor Design
Analyze forces between stator windings and optimize motor construction for mechanical stability.
Transformer Engineering
Calculate forces between primary and secondary windings to ensure proper mechanical support and spacing.
Magnetic Force Between Wires Formulas
Our calculator employs scientifically validated formulas based on Ampère's force law and the Biot-Savart law. Understanding these calculations helps engineers design safe and efficient electrical systems.
📊 Core Calculation Formulas
Force Per Unit Length
Fundamental formula for force per meter between parallel wires
Total Force
Total force over a given wire length
Magnetic Field from Wire
Magnetic field strength at distance d from a current-carrying wire
Force Direction Rule
Opposite direction currents → Repulsion
Right-hand rule determines force direction between parallel wires
❓ Frequently Asked Questions
What is Ampère's force law?
Ampère's force law describes the magnetic force per unit length between two parallel current-carrying wires. The force per meter is given by F/L = μ₀I₁I₂/(2πd), where μ₀ is the permeability of free space, I₁ and I₂ are the currents, and d is the separation distance.
When do wires attract and when do they repel?
Wires attract when currents flow in the same direction and repel when currents flow in opposite directions. This is determined by the right-hand rule: parallel currents create magnetic fields that interact to produce attraction, while anti-parallel currents produce repulsion.
How does distance affect the magnetic force?
The force is inversely proportional to the distance between wires. Doubling the distance reduces the force by half. This relationship follows the 1/d dependence in Ampère's law, making wire spacing critical in power transmission and motor design.
What is the significance of force per unit length?
Force per unit length (F/L) is independent of the total wire length and represents the fundamental interaction strength. It's useful for comparing different configurations and is the basis for calculating total force by multiplying by wire length.
How do I calculate force for non-parallel wires?
For non-parallel wires, the calculation becomes more complex and requires vector analysis. The force depends on the angle between wires and requires integration along the wire length. This calculator focuses on parallel wire configurations, which are most common in practical applications.
What is relative permeability and when does it matter?
Relative permeability (μᵣ) accounts for magnetic materials between or around the wires. For air and vacuum, μᵣ = 1. In ferromagnetic materials, μᵣ can be much higher, significantly increasing the magnetic force. This is important in transformer cores and magnetic circuit design.
How is this force relevant to power transmission lines?
In high-voltage transmission lines, magnetic forces between parallel conductors can cause mechanical stress, vibration, and potential damage. Engineers must calculate these forces to design proper spacing, support structures, and damping systems to ensure safe and reliable operation.
📚 Official Data Sources
This calculator uses verified data and formulas from the following authoritative sources:
NIST Physical Constants
https://physics.nist.gov/cuu/Constants/Fundamental physical constants database
Last Updated: 2026-02-01
Griffiths - Introduction to Electrodynamics
https://www.pearson.com/Standard electromagnetism textbook (4th Edition)
Last Updated: 2017-01-01
HyperPhysics - Ampère's Force Law
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/forwir.htmlEducational resource on force between wires
Last Updated: 2026-02-06
Physics LibreTexts - Magnetic Forces
https://phys.libretexts.org/Open educational resource for physics
Last Updated: 2026-02-06
Jackson - Classical Electrodynamics
https://www.wiley.com/Advanced electromagnetism reference (3rd Edition)
Last Updated: 1998-01-01
⚠️ Disclaimer
Important: This calculator provides estimates for magnetic forces between parallel current-carrying wires based on Ampère's force law. Actual forces may vary due to:
- Non-parallel wire configurations requiring vector analysis
- Proximity effects and edge effects in real-world geometries
- AC current effects including skin effect and proximity losses
- Magnetic material properties and saturation effects
- Temperature variations affecting conductor properties
Always consult with qualified electrical engineers and follow applicable electrical codes and safety standards when designing power systems, motors, or transformers. This calculator is for educational and preliminary design purposes only.
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