Ampère's law lab for AP Physics C: practical with sample results (free PDF download)

Quick answer: The Biot–Savart law gives the field of a current element, dB = (μ₀/4π) I dl × r̂/r², and integrating it yields B = μ₀I/2πd for a long wire and μ₀I/2R at a loop's centre. This AP Physics C lab on Ampère's law gives the aim, the equipment, the safety points, a step-by-step method, sample results and 7 analysis questions; the answers are on a separate page and the lab sheet is a free printable PDF.

Does the field inside a solenoid grow in proportion to the current, and does the gradient match the number of turns per metre? You will wind a simple coil, measure its axial field with a phone magnetometer, and use the straight-line graph to test B = μ₀nI.

Level: AP Physics C (Mechanics and E&M, calculus-based) · Curriculum: AP PC:E&M Unit 12

Aim

Measure the magnetic field inside a long solenoid for several currents and use the gradient of the B against I graph to test B = μ₀nI.

Equipment

Cardboard tube about 20 cm long and 4 cm across
Enamelled copper wire, 0.5 mm, 200 turns wound evenly
Smartphone with a magnetometer app (reads in μT)
Ammeter, rheostat of about 10 Ω and a 3 V supply (two 1.5 V cells)
Ruler and tape

Safety

The coil warms up: switch on only for a few seconds per reading and keep I below 1.5 A. Do not short the cells. Keep the phone away from any water and remove cards with magnetic strips.

Method

Wind 200 turns in one layer along 20 cm and count n = turns/length.
Place the phone’s sensor at the centre of the tube with its axis along the coil’s axis.
With the current off, record the background field B₀ (about 48 μT here).
Set I = 0.20 A with the rheostat, switch on, read B, then switch off.
Repeat for 0.40, 0.60, 0.80, 1.00 and 1.20 A.
Reverse the supply once at I = 1.0 A and compare to remove the background.