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 AP Physics 2 worksheet on coulomb's law gives 20 problems from easy to hard: counting electrons, charging by friction and attract or repel. The worked answers are on a separate page, and the worksheet is a free printable PDF.
These problems train the ideas of AP Physics 2 unit 10 on charge and electric force: counting charge, conservation, charging methods, Coulomb’s law and the addition of forces. They run from one-step calculations to multi-part reasoning of the kind used in free-response questions. Use k = 8.99 × 10⁹ N·m²/C² and e = 1.60 × 10⁻¹⁹ C, and write units with every answer.
Level: AP Physics 2 (algebra-based) · Curriculum: AP P2 Unit 10
Problem 1 Counting electrons ★★★
A plastic comb in Pune carries an excess of 2.0 × 10¹³ electrons. Use e = 1.60 × 10⁻¹⁹ C.1. State the sign of the charge on the comb.
2. Then calculate the magnitude of its charge.
3. Finally, calculate how many electrons must be added to give a charge of −1.0 μC.
Problem 2 Charging by friction ★★★
Rubbing with wool transfers 5.0 × 10¹⁰ electrons to a plastic ruler.1. Calculate the charge on the ruler.
2. Then state the charge on the wool.
3. Finally, state the total charge of ruler and wool and name the law.
Problem 3 Attract or repel ★★★
State whether the force between each pair is attractive, repulsive or (for a neutral object) a weak attraction, and give a reason.1. positive and positive
2. negative and positive
3. negative rod and a neutral metal ball
Problem 4 A simple Coulomb force ★★★
Two small spheres carrying +4.0 μC and +6.0 μC are 0.50 m apart.1. Calculate the force on each sphere.
2. Then state whether the force is attractive or repulsive.
3. Finally, state the direction of the force on the +4.0 μC sphere.
Problem 5 Unit conversions ★★★
Convert each quantity to the unit shown.1. 3.5 μC to coulombs
2. 250 nC to coulombs
3. 4.0 cm to metres
4. 0.75 mC to microcoulombs
Problem 6 Inverse-square scaling ★★★
Two charges exert a force of 12 N on each other when 2.0 cm apart.1. Find the force when they are 4.0 cm apart.
2. Then find the force when they are 1.0 cm apart.
3. Finally, find the force when they are 6.0 cm apart.
Problem 7 Changing charge and distance ★★★
Two charged spheres exert a force of 0.90 N on each other at a distance r.1. One charge is doubled and r is tripled. Find the new force.
2. Both charges are doubled and r is halved. Find the new force.
3. One sphere is discharged to zero. State the force.
Problem 8 Charging by induction ★★★
Bilal holds a positively charged glass rod near, but not touching, a neutral metal sphere on an insulating stand.1. Describe how charge moves in the sphere.
2. While the rod stays there, he touches the sphere with a finger for a moment. Describe the flow of charge.
3. He removes the finger and then the rod. State the final sign of the charge on the sphere and explain.
Problem 9 Electroscope ★★★
Mei brings a negative rod near the disc of a neutral gold-leaf electroscope (shown).2. The rod is moved away without touching. Describe what the leaves do and why.
3. Finally, repeat, but the rod touches the disc before it is removed. Predict the leaves afterwards.
Problem 10 Comb and paper ★★★
Emma rubs a plastic comb on her hair and holds it above small pieces of neutral paper. The paper jumps up to the comb.1. Explain why a neutral piece of paper is attracted.
2. Then explain why the attraction is stronger than the repulsion.
3. After a moment some pieces fall off again. Suggest why.
Problem 11 Finding an unknown charge ★★★
Two identical small spheres 0.10 m apart repel each other with a force of 2.7 N.1. Write an expression for the charge q on each sphere.
2. Then calculate q.
Problem 12 Net force on a line ★★★
A +6.0 μC charge sits at x = 0 and a +2.0 μC charge sits at x = 0.40 m. A −1.0 μC charge is placed at x = 0.10 m.1. Calculate the force from the +6.0 μC charge.
2. Then calculate the force from the +2.0 μC charge.
3. Finally, state the net force with direction.
Problem 13 Sharing charge ★★★
Two identical metal spheres carry +8.0 μC and −2.0 μC. They are 0.20 m apart.1. Calculate the force between them.
2. They are touched together and returned to 0.20 m apart. Calculate the new charge on each.
3. Finally, calculate the new force and say whether it is attractive.
Problem 14 Electric force in hydrogen ★★★
In a hydrogen atom an electron orbits a proton at a distance of 5.3 × 10⁻¹¹ m. Use me = 9.11 × 10⁻³¹ kg, mp = 1.67 × 10⁻²⁷ kg and G = 6.67 × 10⁻¹¹ N·m²/kg².1. Calculate the electric force between them.
2. Then calculate the gravitational force between them.
3. Finally, calculate the ratio of the two forces.
Problem 15 Force against 1/r² graph ★★★
Kofi measures the force between two small spheres of equal charge at four separations and plots F against 1/r² (graph shown).2. Then find the gradient using the point at 1/r² = 100 m⁻².
3. Finally, calculate the charge on each sphere.
Problem 16 Zero-force point ★★★
A +4.0 μC charge and a +1.0 μC charge are fixed 0.30 m apart on a line. A small third charge is placed between them so that it feels no net force.1. Explain why the third charge must lie between them.
2. Then calculate its distance from the +4.0 μC charge.
3. Finally, state whether the sign of the third charge matters.
Problem 17 Hanging charged balls ★★★
Two identical balls, each of mass 2.0 g, hang from the same point on threads 1.00 m long. They are given equal charges and settle with their centres 0.10 m apart (shown, not to scale).2. Then show that the electric force on each ball is F = mg tanθ and calculate it.
3. Finally, calculate the charge on each ball.
Problem 18 Forces in two dimensions ★★★
A +4.0 μC charge is at (0, 0) and a −4.0 μC charge is at (0.40 m, 0). A +2.0 μC charge q₃ is at (0.20 m, 0.15 m) (shown).2. Then calculate the size of the force each charge exerts on q₃.
3. Finally, find the net force on q₃, giving direction.
Problem 19 Hovering sphere ★★★
A fixed sphere carries +25 nC. A sphere of mass 0.40 g carrying +25 nC floats at rest directly above it.1. Explain why the upper sphere can stay still.
2. Then calculate the weight of the upper sphere.
3. Finally, calculate the separation of the spheres.
Problem 20 Unequal charges and motion ★★★
A charge +Q of mass m and a charge +4Q of mass 4m are released from rest, close together, in space far from anything else.1. Compare the sizes of the forces on the two charges and justify your answer.
2. Then compare their initial accelerations.
3. Finally, describe the motion of their centre of mass.
