Derive an expression for the force per unit length between two long straight parallel wires carrying currents. Use it to define one ampere.

1. 1 · Start from the field of a wire. Wire 1 makes B₁ = μ₀I₁/2πr at wire 2, at right angles to it.
2. 2 · Draw the wires. [Two vertical wires r apart with upward currents I₁ and I₂; B₁ shown as ⊗ at wire 2; the force on each wire pointing towards the other]
3. 3 · Find the force. A length l of wire 2 feels F = B₁I₂l = μ₀I₁I₂l/2πr, so F/l = μ₀I₁I₂/2πr.
4. 4 · Give the direction. By Fleming's left-hand rule, currents in the same direction attract and opposite currents repel.
5. 5 · Define the ampere. With I₁ = I₂ = 1 A and r = 1 m, F/l = 2 × 10⁻⁷ N m⁻¹. One ampere is the current in each wire that gives this force.
6. 6 · Close in one line. So, the force depends on the product of the currents and falls as the distance grows.

Scoring tip: In the definition, say 'long, straight, parallel', '1 m apart', 'in vacuum' and '2 × 10⁻⁷ N per metre'. Each phrase carries marks.