State Ampere's circuital law. Apply it to a long, tightly wound solenoid with n turns per metre, carrying a current I, to find the field inside it.
How to lay out the answer. Follow the frame, then write it in your own words.
1 · State the law. ΣB·Δl round any closed loop = μ₀ × the total current through the loop.
2 · Draw the solenoid. [A long solenoid in section: ⊙ along the top row, ⊗ along the bottom; straight field lines inside; a rectangle abcd with ab = l inside along the axis and cd outside]
3 · Add B·Δl round the rectangle. Along ab: Bl. Along cd: zero, as B ≈ 0 outside. Along bc and da: zero, as B is zero or at right angles to the path. Total = Bl.
4 · Find the current enclosed. The rectangle holds nl turns, each carrying I, so the current through it is nlI.
5 · Apply the law. Bl = μ₀nlI, so B = μ₀nI, uniform and along the axis.
6 · Link to life. With a soft iron core, such a solenoid is the electromagnet of a doorbell or a scrap-yard crane.
7 · Close in one line. So, the field inside depends only on the turns per metre and the current.
Scoring tip: Explain why each of the four sides gives Bl or zero. Most of the marks are in that step.
