Force between two parallel current-carrying wires
Magnetic field and forces · Physics
DC circuit
Interactive 3DElectrons drift around the loop — raise the voltage and watch the current obey Ohm's law.
Controls
Drag the sliders or type a value — the simulation updates live.
Study notes
Worked example: Two long parallel wires 5 cm apart carry 10 A and 15 A in the same direction. (a) Find the force per metre on each. (b) Attractive or repulsive? (c) What force acts on a 2 m length? Step 1: F/l = μ0I1I2/2πr = (4π × 10⁻⁷ × 10 × 15)/(2π × 0.05) = (6π × 10⁻⁵)/(0.1π) = 6 × 10⁻⁴ N/m = 0.6 mN/m. Step 2: Same direction → attractive; each wire is pulled toward the other with 0.6 mN per metre. Step 3: On 2 m: F = 1.2 mN. Step 4: Scale-up: at 10 kA each (fault condition), F/l = (4π×10⁻⁷×10⁸)/(2π×0.05) = 40 N/m — forty newtons per metre, enough to rip poorly braced busbars off their insulators. This is why substation design is mechanical as well as electrical.