State Ampere's circuital law. Use it to find the magnetic field due to an infinitely long straight current-carrying wire, and show how the field varies with distance.

1. 1 · State the law. ∮ B·dl = μ₀I: the line integral of B round a closed loop equals μ₀ times the current through it.
2. 2 · Choose the Amperian loop. [Wire with current I; circle of radius r centred on it and perpendicular to it; B along the tangent at a point]
3. 3 · Use symmetry. B is tangential and has the same size everywhere on the circle, so ∮ B·dl = B × 2πr.
4. 4 · Apply the law. B × 2πr = μ₀I, so B = μ₀I/2πr.
5. 5 · Show the variation. B ∝ 1/r: sketch a falling curve of B against r.
6. 6 · Close in one line. So, the field of a long straight wire is μ₀I/2πr, in circles given by the right-hand thumb rule.

Scoring tip: Draw the Amperian loop and write the word 'symmetry'. Without it, B cannot be taken out of the integral.