The questions are on the coulomb's law test. Take it under real conditions before reading the mark scheme.
Quick answer: Electric charge comes in positive and negative kinds, is conserved and is quantised in units of e = 1.60 × 10⁻¹⁹ C. This mark scheme gives the model answers and the marks for the 8 questions of the AP Physics 2 test on coulomb's law, from glass rod and silk to electric and gravitational forces, with the equivalent answers to accept.
Award marks as shown for method, substitution and answer. In explanation questions, accept any wording that gives the correct physical idea. Do not penalise the same unit mistake twice, and allow answers within 2 % of the values given.
Level: AP Physics 2 (algebra-based) · Curriculum: AP P2 Unit 10
Question 1 Glass rod and silk (2 marks)
(a) Q = Ne = 3.0 × 10¹⁰ × 1.60 × 10⁻¹⁹ = +4.8 × 10⁻⁹ C.
(b) −4.8 × 10⁻⁹ C, because charge is conserved.
Marking: 1 mark for each part, including sign and unit.
Question 2 Attractive force (3 marks)
F = (8.99 × 10⁹)(2.0 × 10⁻⁶)(6.0 × 10⁻⁶) / (0.15)² = 0.1079 / 0.0225 = 4.8 N, attractive on both charges.
Marking: 1 mark for correct substitution in SI units; 1 mark for the value; 1 mark for stating attractive.
Question 3 Tripling the distance (2 marks)
The force is inversely proportional to r², so it is divided by 3² = 9. F = 0.90 / 9 = 0.10 N.
Marking: 1 mark for the inverse square relation; 1 mark for the value.
Question 4 Induction (3 marks)
The rod repels electrons in the sphere to the far side, so the near side is positive. The sphere is briefly connected to the earth, which lets electrons flow away. The earth connection is removed first and then the rod, leaving a net positive charge.
Marking: 1 mark for charge separation; 1 mark for earthing; 1 mark for removing earth before the rod.
Question 5 Balanced forces (3 marks)
From the +4.0 μC charge: F = (8.99 × 10⁹)(4.0 × 10⁻⁶)(1.0 × 10⁻⁶) / (0.20)² = 0.90 N towards −x. From the +1.0 μC charge: F = (8.99 × 10⁹)(1.0 × 10⁻⁶)(1.0 × 10⁻⁶) / (0.10)² = 0.90 N towards +x. The forces are equal and opposite, so the net force is 0 N.
Marking: 1 mark for each force with direction; 1 mark for the conclusion.
Question 6 Touching spheres (2 marks)
The total charge is +6.0 μC and is shared equally, so each sphere has +3.0 μC.
Marking: 1 mark for conservation of charge; 1 mark for equal sharing.
Question 7 Paper and a comb (2 marks)
The comb polarises the paper, so the side of the paper nearer the comb has the opposite charge. That charge is closer, so the attractive force is larger than the repulsion from the more distant like charge. Net attraction.
Marking: 1 mark for polarisation; 1 mark for the distance argument.
Question 8 Electric and gravitational forces (3 marks)
(a) Ratio = ke² / (Gm²) = (8.99 × 10⁹ × 2.56 × 10⁻³⁸) / (6.67 × 10⁻¹¹ × 8.30 × 10⁻⁶¹) = 4.2 × 10⁴².
(b) It does not change, because both forces vary as 1/r² and r cancels.
Marking: (a) 1 mark for the ratio set-up, 1 mark for the value; (b) 1 mark.
