Magnetic Force Between Current-Carrying Wires Calculator

Calculate magnetic force, attraction/repulsion, and field strength between parallel current-carrying conductors

Calculate Magnetic Force Between Wires

Use negative values for opposite current direction

Use negative values for opposite current direction

Center-to-center distance between parallel wires

Length of wire segment to calculate total force

Magnetic Force Analysis Results

2.000 mN
Force per Unit Length
F/L (N/m)
2.000 mN
Total Force
F = (F/L) × L
Attraction
Force Direction
Same direction currents attract

Calculation Details

Formula Used

F/L = (μ₀ × I₁ × I₂) / (2π × d)

Permeability of Free Space

μ₀ = 4π × 10⁻⁷ T⋅m/A

Current 1 (SI)

1.000e+1 A

Current 2 (SI)

1.000e+1 A

Distance (SI)

1.000e-2 m

Wire Length (SI)

1.000e+0 m

Magnetic Field Analysis

B-field from Wire 1 at Wire 2

200.000 μT

B-field from Wire 2 at Wire 1

200.000 μT

B = (μ₀ × I) / (2π × r) - Magnetic field around a straight current-carrying wire

Current Direction & Force Visualization

Same Direction (Attraction)

Wire 1: ——————→ (+I₁)
↑ Attraction Force
|
| d
|
↓ Attraction Force
Wire 2: ——————→ (+I₂)

Parallel currents create attraction

Opposite Direction (Repulsion)

Wire 1: ——————→ (+I₁)
↓ Repulsion Force
|
| d
|
↑ Repulsion Force
Wire 2: ←—————— (-I₂)

Antiparallel currents create repulsion

Example Calculation

High-Voltage Power Lines

Current 1: 1000 A

Current 2: 1000 A (same direction)

Distance: 5 m

Wire length: 100 m

Calculation

F/L = (μ₀ × I₁ × I₂) / (2π × d)

F/L = (4π×10⁻⁷ × 1000 × 1000) / (2π × 5)

F/L = 4×10⁻⁴ / 10 = 4×10⁻⁵ N/m

F = 4×10⁻⁵ × 100 = 4×10⁻³ N

Direction: Attraction

Physics Principles

Ampère's Force Law

F/L = (μ₀I₁I₂)/(2πd)

Force per unit length between parallel wires

Magnetic Field

B = (μ₀I)/(2πr)

Field around straight current-carrying wire

Lorentz Force

F = IL × B

Force on current in magnetic field

Newton's Third Law

F₁₂ = -F₂₁

Equal and opposite forces on both wires

Quick Reference

Same direction currents attract each other

Opposite direction currents repel each other

Force is proportional to both currents

📏

Force decreases with distance between wires

🧲

Based on magnetic field interaction

Understanding Magnetic Force Between Current-Carrying Wires

Physical Mechanism

When electric current flows through a conductor, it creates a magnetic field around the wire. When two current-carrying wires are placed near each other, each wire experiences a force due to the magnetic field created by the other wire. This is a manifestation of the Lorentz force.

Ampère's Force Law

  • Force per unit length: F/L = (μ₀I₁I₂)/(2πd)
  • Proportional to product of currents
  • Inversely proportional to distance
  • Depends on permeability of medium

Force Direction Rules

Attraction (Same Direction)

  • • Both currents in same direction
  • • Magnetic fields reinforce between wires
  • • Creates low-pressure region
  • • Wires are pulled together

Repulsion (Opposite Direction)

  • • Currents in opposite directions
  • • Magnetic fields oppose between wires
  • • Creates high-pressure region
  • • Wires are pushed apart

⚠️ Engineering Applications

  • • Power transmission line design
  • • Electric motor operation
  • • Transformer winding layout
  • • Magnetic levitation systems

✓ Important Constants

  • • μ₀ = 4π × 10⁻⁷ T⋅m/A
  • • Permeability of free space
  • • Fundamental physical constant
  • • Defines magnetic unit system

📋 Key Assumptions

  • • Wires are straight and parallel
  • • Wires are infinitely long
  • • Current is uniformly distributed
  • • Medium is non-magnetic (μ = μ₀)