The questions are on the magnetic force test. Take it under real conditions before reading the mark scheme.
Quick answer: A moving charge or a current produces a magnetic field, and a magnetic field pushes sideways on other moving charges. This mark scheme gives the model answers and the marks for the 8 questions of the AP Physics 2 test on magnetic force, from field near a cable to undeflected beam, with the equivalent answers to accept.
The marking guide gives one mark for the correct relationship, one for the substitution and one for the answer with its unit. Direction questions require the rule to be named or applied, not just a final word.
Level: AP Physics 2 (algebra-based) · Curriculum: AP P2 Unit 12
Question 1 Field near a cable (2 marks)
(a) B = μ₀I/2πr = (4π × 10⁻⁷)(25) / (2π × 0.040) = 1.3 × 10⁻⁴ T.
(b) Current doubles and distance doubles, so B is unchanged: 1.3 × 10⁻⁴ T.
Marking: 1 mark each part.
Question 2 Direction of force (2 marks)
(a) With north as the direction of v and east as B, the right-hand rule gives downward for a proton.
(b) The electron is negative, so the force is upward.
Marking: 1 mark each part.
Question 3 Proton in a uniform field (4 marks)
(a) F = qvB = (1.6 × 10⁻¹⁹)(1.2 × 10⁶)(0.80) = 1.5 × 10⁻¹³ N.
(b) qvB = mv²/r, so r = mv/(qB) = (1.67 × 10⁻²⁷)(1.2 × 10⁶) / (1.6 × 10⁻¹⁹ × 0.80) = 1.6 cm.
(c) r is proportional to v, so the radius doubles.
Marking: (a) 1; (b) 1 for the relationship, 1 for the answer; (c) 1.
Question 4 Force on a wire (3 marks)
(a) F = BIL = 0.15 × 6.0 × 0.80 = 0.72 N.
(b) F = 0.72 × sin 40° = 0.72 × 0.643 = 0.46 N.
(c) The force on the moving charges depends on the component of the velocity perpendicular to B. Along the field there is no such component, so F = 0.
Marking: 1 mark each part.
Question 5 Parallel wires (3 marks)
(a) F/L = μ₀I₁I₂/2πd = (4π × 10⁻⁷)(12)(8.0) / (2π × 0.030) = 6.4 × 10⁻⁴ N/m.
(b) Currents in the same direction attract.
Marking: (a) 1 for substitution, 1 for the answer; (b) 1.
Question 6 Work done (2 marks)
The magnetic force is always perpendicular to the velocity, so it has no component along the displacement and does zero work. With no work done, the kinetic energy and the speed stay constant, and only the direction changes.
Marking: 1 for perpendicular force; 1 for zero work so no change of speed.
Question 7 Sign of the charge (2 marks)
For a positive charge moving right in a field out of the page, the right-hand rule gives a downward force. The path curves upward, the opposite way, so the charge is negative.
Marking: 1 for correct application of the rule; 1 for stating negative.
Question 8 Undeflected beam (2 marks)
(a) qE = qvB, so v = E/B = 6.0 × 10³ / 0.030 = 2.0 × 10⁵ m/s.
(b) For a faster particle the magnetic force qvB is larger than the electric force qE, so it is deflected in the direction of the magnetic force.
Marking: 1 mark each part.
