The shape of the lesson
By the end of the lesson, learners can
- Charges, distance, force: Vary the two charges and their separation.
- An inverse-square law: Because the force depends on 1/r², moving the charges twice as far apart cuts the force to a quarter.
- Uniform field: E = V / d; the force on a charge is F = qE, and a charge crossing the field follows a parabola.
- Point charges: Coulomb's law F = Q₁Q₂ / (4πε₀r²) and field E = Q / (4πε₀r²) are both inverse-square.
- Potential: V = Q / (4πε₀r) falls off as 1/r; the work to move charge q is W = qΔV, and E = −dV/dr.
One picture every idea returns to
Two point charges exert equal and opposite forces given by Coulomb’s law, F = Q₁Q₂ / (4πε₀r²). Like charges repel, opposite charges attract, and the force falls off with the square of the separation.
Forty-five minutes, phase by phase
| Time | Phase | What happens in the room | Grouping |
|---|---|---|---|
| 0 to 5 min | Hook: predict | Open with the question in the title, The force between point charges.. Coulomb’s law is the electric twin of Newton’s law of gravitation: same inverse-square shape, but charges can repel as well as attract. Put the figure on the board: it is the one picture every idea in the lesson returns to. | Whole class, then pairs |
| 5 to 17 min | Teach and check: Charges, distance, force | Vary the two charges and their separation. Project tab 3 of the lab (Coulomb’s law) and let a student drive it while the class predicts. | Whole class, then pairs |
| 17 to 30 min | Teach and check: An inverse-square law | Because the force depends on 1/r², moving the charges twice as far apart cuts the force to a quarter. | Frayer Model |
| 30 to 43 min | Check and plenary | The quick-check questions from the student lesson, answered on mini whiteboards one at a time; re-teach the one most get wrong, then a random call on the last. | Individual, then whole class |
| 43 to 45 min | Exit and homework | Set the worksheet below (4 questions, 46 marks) from the topic practice set. Learners self-assess against the objectives before they leave. | Individual |
Protect the parts that carry the learning
The sequence carries about fifty minutes of material, so the lab is driven by one student while the class predicts rather than explored freely. Times are a guide.
Protected: the check at 30 minutes. It is the only individual read on whether the key idea landed, and it is not cut.
Cut first if the build overruns: the last check in An inverse-square law, never the check or the plenary.
In a 60 minute block: run worksheet questions 1 to 3 in class as a Rally Coach set and model both the hardest worked example and its check live.
Frayer Model
Pairs fill a four-box grid for the key term: definition, characteristics, examples and non-examples. The non-examples box is where the misconceptions surface, so give it the most time.
The full structure, with its variations and the other twelve, is on the cooperative-learning page.
What to head off, and how
No examiner trap is recorded for this lesson. Use the quiz key below to spot the distractor most of the class picks.
Coulomb’s law: topic worksheet
4 questions, 46 marks. Written in the style of the papers; no past paper question is reproduced. These questions cover the whole topic, so sibling lessons share them.
Two small charged spheres carry charges Q₁ = +2.0 × 10⁻⁸ C and Q₂ = −3.0 × 10⁻⁸ C. Their centres are 4.0 cm apart, as shown in Fig. 2.1.
(a) State Coulomb's law. [2]
(b) Calculate the magnitude of the force between the spheres and state whether it is attractive or repulsive. [3]
(c) State how the force would change if the separation were halved. [2]
(d) Calculate the electric field strength due to Q₁ alone at the position of Q₂. [3]
(e) Hence verify, using F = Q₂E, the force found in (b). [2]
(f) State why a uniformly charged sphere can be treated as a point charge at its centre. [1]
Two small charges, +3.0 nC and +5.0 nC, are placed 2.0 cm apart in a vacuum.
(a) State Coulomb’s law. [2]
(b) Calculate the force between the charges. [3]
(c) State whether the force is attractive or repulsive. [1]
(d) State the effect on the force of doubling the separation. [2]
(e) Calculate the separation at which the force would be 1.0 × 10⁻⁴ N. [2]
A point charge Q = +4.0 nC is fixed in a vacuum. This question links Coulomb’s law with the field of a point charge.
(a) A second charge q = +2.0 nC is placed 3.0 cm from Q. Calculate the force on it. [3]
(b) Write the expression for the electric field strength due to a point charge. [1]
(c) Calculate the field strength at 3.0 cm from Q. [2]
(d) Using your answer to (c), show that the force in (a) equals qE. [2]
(e) State and explain how the field strength changes at a distance of 6.0 cm. [2]
(f) State the direction of the field at the point. [1]
Two point charges, A = +5.0 nC and B = −5.0 nC, are fixed 8.0 cm apart in a vacuum. P is the midpoint, as shown in Fig. 10.1. This question uses field strength, Coulomb’s law, the field of a point charge, and potential.
(a) Define electric field strength. [1]
(b) Calculate the force between A and B. [2]
(c) Calculate the field strength at P due to each charge, and the resultant field at P. [4]
(d) Calculate the electric potential at P. [3]
(e) State what your answer to (d) implies about the work done in bringing a charge to P from infinity. [2]
Answer key and marking notes
- (a)The force between two point charges is proportional to the product of the charges and inversely proportional to the square of their separation ✓, directed along the line joining them ✓
- (b)F = Q₁Q₂ / (4πε₀r²) = 8.99 × 10⁹ × (2.0 × 10⁻⁸)(3.0 × 10⁻⁸) / (0.040)² ✓✓ = 3.4 × 10⁻³ N, attractive (opposite signs) ✓
- (c)It would become four times as large ✓, since F ∝ 1/r² ✓
- (d)E = Q₁ / (4πε₀r²) = 8.99 × 10⁹ × 2.0 × 10⁻⁸ / (0.040)² ✓✓ = 1.1 × 10⁵ V m⁻¹ ✓
- (e)F = Q₂E = 3.0 × 10⁻⁸ × 1.12 × 10⁵ ✓ = 3.4 × 10⁻³ N, the same as (b) ✓
- (f)Outside the sphere its field is identical to that of a point charge of the same value placed at its centre ✓
- (a)The force between two point charges is proportional to the product of the charges and inversely proportional to the square of their separation ✓✓
- (b)F = Q₁Q₂/(4πε₀r²) = 8.99 × 10⁹ × (3.0 × 10⁻⁹)(5.0 × 10⁻⁹)/(0.020)² ✓✓ = 3.4 × 10⁻⁴ N ✓
- (c)Repulsive (the charges have the same sign) ✓
- (d)The force falls to one quarter (inverse-square law) ✓✓
- (e)F ∝ 1/r², so r = 0.020 × √(3.37/1.0) ✓ = 3.7 × 10⁻² m ✓
- (a)F = 8.99 × 10⁹ × (4.0 × 10⁻⁹)(2.0 × 10⁻⁹)/(0.030)² ✓✓ = 8.0 × 10⁻⁵ N ✓
- (b)E = Q/(4πε₀r²) ✓
- (c)E = 8.99 × 10⁹ × 4.0 × 10⁻⁹/(0.030)² ✓ = 4.0 × 10⁴ V m⁻¹ ✓
- (d)qE = 2.0 × 10⁻⁹ × 4.0 × 10⁴ = 8.0 × 10⁻⁵ N ✓, which matches the force in (a) ✓
- (e)It falls to one quarter, 1.0 × 10⁴ V m⁻¹ ✓, because E ∝ 1/r² ✓
- (f)Radially outward from Q (a positive charge) ✓
- (a)The force per unit positive charge at a point ✓
- (b)F = 8.99 × 10⁹ × (5.0 × 10⁻⁹)²/(0.080)² ✓ = 3.5 × 10⁻⁵ N (attractive) ✓
- (c)Each at r = 0.040 m: E = 8.99 × 10⁹ × 5.0 × 10⁻⁹/(0.040)² = 2.8 × 10⁴ V m⁻¹ ✓✓; at P both fields point from A toward B, so they add: resultant = 5.6 × 10⁴ V m⁻¹ ✓✓
- (d)V = ΣQ/(4πε₀r) = 8.99 × 10⁹ × (5.0 × 10⁻⁹/0.040 − 5.0 × 10⁻⁹/0.040) ✓✓ = 0 V ✓
- (e)No net work is needed, since the potential at P is zero ✓✓
The lesson's own checks as a quiz
The quick-check and exam-style questions from the student lesson, printable with the key.
Coulomb’s law states that the force between two point charges is:
- Aproportional to the product of the charges and inversely proportional to r²
- Bproportional to r²
- Cproportional to the sum of the charges
- Dindependent of distance
Doubling the separation of two point charges changes the force to:
- Aone quarter
- Bone half
- Cdouble
- Dfour times
Two point charges of the same sign:
- Arepel each other
- Battract each other
- Cexert no force
- Dalways touch
Outside its surface, a uniformly charged sphere behaves like:
- Aa point charge at its centre
- Ba uniform field
- Can uncharged object
- Da dipole
Quiz key
F = Q₁Q₂ / (4πε₀r²): proportional to the product of the charges, inverse-square in separation.
F ∝ 1/r², so doubling r multiplies the force by 1/4.
Like charges repel; only opposite charges attract.
The external field of a uniformly charged sphere is identical to that of a point charge of the same value at its centre.
What to project
The student lesson embeds these tabs. Open them full screen on the projector; every slider has a drag handle on the stage.
Slides for this lesson
A projectable deck for every pack is on the way. Until then, present the student lesson full screen: its sections, figure and lab tabs follow the same order as the plan above.