The questions are on the electric potential test. Take it under real conditions before reading the mark scheme.
Quick answer: Electric potential is potential energy per unit charge, V = U/q, measured in volts. This mark scheme gives the model answers and the marks for the 8 questions of the AP Physics C test on electric potential, from meaning of potential to energy of a charge, with the equivalent answers to accept.
Award marks as shown. Accept answers within rounding, and give full credit for a correct method with a transcription slip carried through. Penalise a missing unit once only.
Level: AP Physics C (Mechanics and E&M, calculus-based) · Curriculum: AP PC:E&M Unit 9
Question 1 Meaning of potential (2 marks)
Potential is the electric potential energy per unit charge at a point (V = U/q). A 12 V difference means 12 J of work per coulomb to move charge between the points.
Marking: 1 mark for energy per unit charge; 1 mark for 12 J/C interpretation.
Question 2 Point charge (2 marks)
V = kq/r = (8.99 × 10⁹)(−6.0 × 10⁻⁹)/0.20 = −2.7 × 10² V.
Marking: 1 mark for substitution with the negative sign; 1 mark for the answer with unit.
Question 3 Reading the graph (3 marks)
a. |E| = ΔV/Δx = 6/0.30 = 20 V/m, in the +x direction because V falls.
b. The slope is zero, so E = 0 there.
Marking: (a) 1 mark for the magnitude, 1 for the direction; (b) 1 mark for zero slope hence zero field.
Question 4 Integrating a field (3 marks)
ΔV = −∫ from 0 to 0.10 of 4.0 × 10³ x dx = −2.0 × 10³ (0.10)² = −20 V.
Marking: 1 mark for the integral set-up, 1 for evaluation, 1 for the sign and unit.
Question 5 Equipotentials (2 marks)
No work is done moving a charge along an equipotential, so the field has no component along it. The field is therefore perpendicular to the surface.
Marking: 1 mark for zero work along the surface; 1 mark for no tangential component.
Question 6 Conducting sphere (3 marks)
(a) V = kQ/R = (8.99 × 10⁹)(2.0 × 10⁻⁸)/0.10 = 1.8 × 10³ V.
(b) Same as the surface, 1.8 × 10³ V.
(c) E = 0 in the interior of the conductor.
Marking: 1 mark each part.
Question 7 Ring on its axis (3 marks)
s = √(0.30² + 0.40²) = 0.50 m, so V = kQ/s = 36 V. Every piece of charge is at distance s and potential adds as a scalar.
Marking: 1 mark for s; 1 mark for the value with unit; 1 mark for the scalar explanation.
Question 8 Energy of a charge (2 marks)
½mv² = eΔV, so v = √(2 × 1.60 × 10⁻¹⁹ × 500/1.67 × 10⁻²⁷) = 3.1 × 10⁵ m/s.
Marking: 1 mark for the energy equation; 1 mark for the answer.
