Magnetic Force Between Wires
Calculate the magnetic force between two parallel current-carrying wires using Ampère's force law F/L = μ₀I₁I₂/(2πd). Free online electromagnetism calculator with instant results, interactive charts, and detailed breakdowns for physics students and engineers.
About This Calculator
The Magnetic Force Between Wires calculator computes the electromagnetic force between two parallel, straight, current-carrying wires using Ampère's force law. This fundamental physics principle explains why power cables and electrical wires experience forces when carrying current near each other. The calculator is essential for physics students studying electromagnetism, electrical engineers designing busbars and transmission lines, and hobbyists working with high-current circuits.
The calculation uses the formula F = μ₀ × I₁ × I₂ × L / (2π × d), where μ₀ = 4π × 10⁻⁷ H/m is the vacuum permeability, I₁ and I₂ are the currents in amperes, L is the length of the wire segment in meters, and d is the separation distance in meters. The calculator also displays the force per unit length and indicates whether the wires attract or repel based on the direction of current flow. Currents flowing in the same direction produce attraction, while opposite directions produce repulsion.
This tool assumes infinitely long, thin, straight, parallel wires in free space — the standard textbook approximation. For real-world applications involving wire thickness, finite lengths, or magnetic materials, additional corrections may apply.
Regional Notes
Global: The formula and constants used are universal physics constants. The ampere (A) is the SI base unit for electric current, and the meter (m) is the SI base unit for distance. These units are standard worldwide.
Frequently Asked Questions
What is the formula for magnetic force between two parallel wires?
The magnetic force per unit length between two parallel current-carrying wires is given by F/L = μ₀I₁I₂/(2πd), where μ₀ is the vacuum permeability (4π × 10⁻⁷ H/m), I₁ and I₂ are the currents in amperes, and d is the distance between the wires in meters.
Do parallel wires attract or repel each other?
Two parallel wires carrying current in the same direction attract each other. When the currents flow in opposite directions, the wires repel each other. This is a consequence of Ampère's force law and the right-hand rule for magnetic fields.
Why does the magnetic force between wires depend on the distance?
The magnetic field produced by a long straight wire decreases with distance according to B = μ₀I/(2πd). Since the force on the second wire depends on the magnetic field strength from the first wire, the force is inversely proportional to the separation distance between the wires.
What is the SI unit of vacuum permeability μ₀?
The vacuum permeability μ₀ has SI units of henries per meter (H/m), which is equivalent to T·m/A (tesla-meters per ampere). Its exact value is defined as 4π × 10⁻⁷ H/m ≈ 1.256637 × 10⁻⁶ H/m.
Can this calculator handle negative currents?
Yes, you can enter positive or negative current values. A positive current indicates one direction of flow, and a negative current indicates the opposite direction. The calculator uses the sign to determine whether the wires attract or repel each other.
How accurate is the magnetic force calculator?
Results are computed using the fundamental Ampère's force law with the standard value of vacuum permeability μ₀ = 4π × 10⁻⁷ H/m. The calculation assumes infinitely long, thin, straight parallel wires in a vacuum, which is the standard textbook model. Results are rounded to 8 decimal places for precision.
What happens if the distance between wires is zero?
If the distance between the wires is zero, the formula would give an infinite force, which is physically impossible. The calculator requires a positive non-zero distance to produce a valid result.