The questions are on the faraday's law test. Take it under real conditions before reading the mark scheme.
Quick answer: Electromagnetic induction produces an emf whenever the magnetic flux Φ = BA cos θ through a loop changes. This mark scheme gives the model answers and the marks for the 8 questions of the AP Physics 2 test on faraday's law, from flux through a coil to loop leaving a field, with the equivalent answers to accept.
Marks are given for the correct relationship, for a correct substitution and for the answer with its unit. In direction questions, explicit reference to the change in flux is needed to reach full marks.
Level: AP Physics 2 (algebra-based) · Curriculum: AP P2 Unit 12
Question 1 Flux through a coil (2 marks)
A = 0.12 × 0.080 = 9.6 × 10⁻³ m². Φ = BA cos θ = 0.25 × 9.6 × 10⁻³ × cos 40° = 1.8 × 10⁻³ Wb.
Marking: 1 for area; 1 for flux with unit.
Question 2 Induced emf (3 marks)
(a) ΔΦ = 1.0 − 4.0 = −3.0 mWb, a magnitude of 3.0 × 10⁻³ Wb.
(b) ε = NΔΦ/Δt = 300 × 3.0 × 10⁻³ / 0.050 = 18 V.
(c) The rate of change doubles, so the emf doubles to 36 V.
Marking: 1 mark each part.
Question 3 Approaching south pole (3 marks)
(a) Clockwise as seen from the magnet.
(b) Approaching the south pole increases the flux through the loop. The loop must oppose this increase, so it produces a south face towards the magnet, which repels it. The right-hand grip rule then gives a clockwise current seen from the magnet.
Marking: (a) 1; (b) 1 for opposing the increase in flux; 1 for the right-hand rule step.
Question 4 Rod on rails (4 marks)
(a) ε = BLv = 0.35 × 0.60 × 2.5 = 0.53 V.
(b) I = ε/R = 0.525 / 1.5 = 0.35 A.
(c) F = BIL = 0.35 × 0.35 × 0.60 = 0.074 N.
(d) P = Fv = 0.0735 × 2.5 = 0.18 W.
Marking: 1 mark each part; allow follow-through.
Question 5 Slow fall in a tube (2 marks)
Aluminium is a conductor, so the moving magnet induces eddy currents in the tube. By Lenz’s law these currents oppose the motion of the magnet, giving an upward force and a smaller acceleration. Plastic is an insulator, so no currents flow and the magnet falls freely.
Marking: 1 for eddy currents induced; 1 for opposing the motion.
Question 6 Faraday’s law in words (2 marks)
The induced emf equals the rate of change of magnetic flux linkage: ε = −NΔΦ/Δt. The minus sign shows that the induced current opposes the change in flux (Lenz’s law, conservation of energy).
Marking: 1 for the statement; 1 for the meaning of the minus sign.
Question 7 Units (2 marks)
Φ = BA, with B in T = N/(A·m). So Wb = T·m² = N·m/A = J/A. Dividing by seconds, Wb/s = J/(A·s) = J/C = V.
Marking: 1 for the unit of Wb in base form; 1 for J/C = V.
Question 8 Loop leaving a field (2 marks)
(a) The flux into the page decreases, so the induced field must also point into the page: the current is clockwise.
(b) The flux changes twice as fast, so the emf doubles.
Marking: 1 mark each part.
