Derive an expression for the force per unit length between two long straight parallel conductors carrying currents. Hence define one ampere.
How to lay out the answer. Follow the frame, then write it in your own words.
1 · Draw the figure. [Two parallel wires 1 and 2, distance d apart, currents in the same direction; B₁ at wire 2 shown as ⊗; forces pointing towards each other]
2 · Field of wire 1 at wire 2. B₁ = μ₀I₁/2πd, perpendicular to wire 2.
3 · Force on a length L of wire 2. F₂₁ = I₂LB₁ = μ₀I₁I₂L/2πd, towards wire 1 (Fleming's left-hand rule).
4 · Force per unit length. f = μ₀I₁I₂/2πd; an equal and opposite force acts on wire 1, so like currents attract.
5 · Define the ampere. With I₁ = I₂ = 1 A and d = 1 m, f = 2 × 10⁻⁷ N/m. One ampere is the current that gives this force.
6 · Real life. Bars carrying large currents in substations are clamped because of these forces.
7 · Close in one line. So, f = μ₀I₁I₂/2πd: attraction for like currents, repulsion for unlike.
Scoring tip: Write the definition of the ampere in full: 'long, straight, parallel, 1 m apart, in vacuum, 2 × 10⁻⁷ N per metre'. Each phrase carries weight.
