Force Between Parallel Currents
Like currents attract; opposite currents repel.
Lesson at a glanceShow the key points
- dF/dl = μ₀i₁i₂/2πd (35.7).
- Same direction: attract; opposite: repel.
- 1 A: wires 1 m apart attract with 2 × 10⁻⁷ N/m.
Each current sits in the other’s magnetic field, so two parallel wires push or pull each other. That force is how the ampere is defined.
The force between parallel wires
Two long parallel wires W₁ and W₂, a distance d apart, carry i₁ and i₂ in the same direction. At an element dl of W₂, the field of W₁ is B = μ₀i₁/2πd (W₂’s own field contributes nothing there). The force on the element is dF = i₂ dl B, and dl⃗ × B⃗ points toward W₁:
The same expression gives the force per length on W₁ due to W₂, as Newton’s third law requires.
Two long parallel wires 2.0 cm apart each carry 4.0 A. Find the force on 25 cm of one of them.
Wires P and Q, 8.0 cm apart, carry 6.0 A and 2.0 A in opposite directions. Where on the line through them is the field zero?
Defining the ampere
For i₁ = i₂ = 1 A and d = 1 m, equation (35.7) gives 2 × 10⁻⁷ N per metre. This was used to define the unit:
- 1Force per length between parallel currents: μ₀i₁i₂/2πd (35.7).
- 2Same direction attract; opposite directions repel.
- 31 A: 2 × 10⁻⁷ N/m between wires 1 m apart.
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