Coulomb's law lab answers for AP Physics 2 (free PDF download)

The method and the results are on the coulomb's law lab. Do the analysis yourself first, then check the answers below.

Quick answer: Electric charge comes in positive and negative kinds, is conserved and is quantised in units of e = 1.60 × 10⁻¹⁹ C. These answers go with the AP Physics 2 lab on coulomb's law: the graph, the calculations, the uncertainties and the conclusion explained, for all 7 analysis questions.

Coulomb’s law lab answers for AP Physics 2 (free PDF download)

The sample readings give a gradient near 3.6 × 10⁻⁶ N·m² and a charge of 20 nC. If your own data differ, check that your graph is straight and passes through the origin, and show every conversion into SI units.

Level: AP Physics 2 (algebra-based) · Curriculum: AP P2 Unit 10

Contents

Question 1 Convert to force

F = Δm g. At 3.0 cm: 0.405 × 10⁻³ × 9.81 = 3.97 × 10⁻³ N. At 8.0 cm: 0.058 × 10⁻³ × 9.81 = 5.7 × 10⁻⁴ N.

Question 2 Calculate 1/r²

r = 0.080, 0.060, 0.050, 0.040, 0.030 m gives 1/r² = 156, 278, 400, 625 and 1111 m⁻². Corresponding forces are 5.7 × 10⁻⁴, 9.9 × 10⁻⁴, 1.46 × 10⁻³, 2.24 × 10⁻³ and 3.97 × 10⁻³ N.

Question 3 Plot and describe

The points lie close to a straight line through the origin, so F is proportional to 1/r², in agreement with Coulomb’s law.

Question 4 Gradient

Gradient = 3.97 × 10⁻³ / 1111 = 3.6 × 10⁻⁶ N·m². It equals kq², the constant in F = kq²/r².

Question 5 Charge on a sphere

q² = 3.6 × 10⁻⁶ / 8.99 × 10⁹ = 4.0 × 10⁻¹⁶ C², so q = 2.0 × 10⁻⁸ C (20 nC).

Question 6 Testing the power law

n = ln(3.97 × 10⁻³ / 5.69 × 10⁻⁴) / ln(8.0 / 3.0) = 1.944 / 0.981 = 1.98, which is very close to 2.

Question 7 Sources of error

Charge leaks into humid air, so the force falls over time and the readings are too low. The charged sphere above also induces charge on the balance pan, changing the force. Improvement: work quickly in dry air and recharge between readings.

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