☰ Contents · Physics

Work of the Ampère force and parallel currents

Lessons 4–5 · 2 lessons · N. Sh. Turdiyev, K. A. Tursunmetov, A. G. Ganiyev, K. T. Suyarov, J. E. Usarov, A. K. Avliyoqulov. Physics Grade 11, 1st edition. Niso Poligraf Publishing House, Tashkent, 2018
5

The force between current-carrying conductors

Textbook: pp. 15–16
GoalCalculate the force between parallel currents with F = μ₀I₁I₂Δl/(2πd) and know the definition of the ampere.
New words
parallel currents · parallel toklarattraction and repulsion · tortishish va itarishishampere · amperinteraction force · o‘zaro ta’sir kuchi
Explanation

Two parallel current-carrying conductors act on each other: the magnetic field of one acts on the other with an Ampère force. If the currents flow in the same direction the conductors attract; if in opposite directions they repel. The force on the second conductor is F = B₁·I₂·Δl with B₁ = μ₀I₁/(2πd); hence F = μ₀I₁I₂Δl/(2πd): the force is proportional to the product of the currents and to the length, and inversely proportional to the distance. The force per unit length is F/Δl = 2·10⁻⁷·I₁I₂/d (N/m, d in metres). The ampere is the constant current which, flowing in two infinitely long parallel conductors of negligible cross-section 1 m apart in vacuum, produces a force of 2·10⁻⁷ N on each metre of their length (the textbook's classical definition; since 2019 the SI defines the ampere through the fixed value of the elementary charge e = 1.602176634·10⁻¹⁹ C, with practically the same result). These forces are tiny, but at hundreds of amperes (for example in busbars) they become noticeable and the strength of the structure must allow for them.

Worked examples
Two parallel wires are 10 cm apart with I₁ = I₂ = 100 A in the same direction. F/Δl = 2·10⁻⁷·100·100/0.1 = 2·10⁻² N/m = 20 mN/m; the wires attract.
Busbars 30 cm apart carry 300 A and 200 A in opposite directions. The force on a 2 m section is F = 2·10⁻⁷·300·200·2/0.3 = 0.08 N; the busbars repel each other.
Class activity

A thought experiment only (do not try it with real wires): sketch two parallel wires and the force directions, then explain how the force changes if one current is reversed. Large currents are dangerous; only a specialist would carry out such an experiment.

Practice
1
Do parallel currents in the same direction attract or repel each other?
2
d = 5 cm, I₁ = I₂ = 50 A. What is the force per unit length in mN/m? (2·10⁻⁷ N/A²)
3
If the distance between wires is halved, by what factor does the force change?
4
Why does the definition of the ampere say «in vacuum» and «infinitely long»?