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
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)
Parallel currents create attraction
Opposite Direction (Repulsion)
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)