The shape of the lesson
By the end of the lesson, learners can
- Potential beside field: Compare the 1/r potential with the 1/r² field for the same point charge.
- Scalar potential, vector field: Potential is a scalar, so potentials from several charges add algebraically (with sign).
- 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
The electric potential at a point is the work done per unit positive charge in bringing it from infinity to that point, V = Q / (4πε₀r). The field is the negative gradient of the potential, E = −dV/dr, and the energy of charge q is Eₙ = qV.
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, Work stored in the field.. Potential is the energy bookkeeping of an electric field. 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: Potential beside field | Compare the 1/r potential with the 1/r² field for the same point charge. Project tab 5 of the lab (Electric potential) and let a student drive it while the class predicts. | Whole class, then pairs |
| 17 to 30 min | Teach and check: Scalar potential, vector field | Potential is a scalar, so potentials from several charges add algebraically (with sign). | Anticipation / Reaction Guide |
| 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 (3 questions, 35 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 Scalar potential, vector field, 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.
Anticipation / Reaction Guide
Before the lesson, students mark five statements true or false. After the teaching they mark them again and justify any change of mind in one sentence each. The statements come from the examiner traps below.
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.
Electric potential: topic worksheet
3 questions, 35 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.
An isolated point charge Q = +6.0 × 10⁻⁹ C sits in a vacuum. Fig. 3.1 shows how the electric potential V varies with distance r from the charge.
(a) Define the electric potential at a point. [2]
(b) Calculate the potential at a distance of 3.0 cm from Q. [2]
(c) State the potential at 6.0 cm from Q, explaining your reasoning. [1]
(d) A charge q = +2.0 × 10⁻⁹ C is moved from 6.0 cm to 3.0 cm from Q. Calculate the work done on it. [3]
(e) State the relationship between the electric field strength and the potential. [2]
(f) State how the electric potential energy of two like point charges varies with their separation. [2]
A point charge Q = +6.0 nC is in a vacuum. This question links the field of a point charge with electric potential.
(a) State what is meant by the electric potential at a point. [2]
(b) Calculate the potential at 5.0 cm from Q. [2]
(c) Calculate the field strength at 5.0 cm from Q. [2]
(d) State the relation between E and V for a radial field, and verify it at 5.0 cm. [2]
(e) Calculate the work done in moving a +2.0 nC charge from 5.0 cm to 10.0 cm from Q. [3]
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 work done per unit positive charge ✓ in bringing it from infinity to that point ✓
- (b)V = Q / (4πε₀r) = 8.99 × 10⁹ × 6.0 × 10⁻⁹ / 0.030 ✓ = 1.8 × 10³ V ✓
- (c)9.0 × 10² V: doubling r halves V, because V ∝ 1/r ✓
- (d)W = qΔV = q(V₃ − V₆) = 2.0 × 10⁻⁹ × (1798 − 899) ✓✓ = 1.8 × 10⁻⁶ J ✓
- (e)The field is the negative gradient of the potential ✓: E = −dV/dr ✓
- (f)The potential energy is positive and proportional to 1/r ✓, falling toward zero as the separation increases ✓
- (a)The work done per unit positive charge in bringing it from infinity to that point ✓✓
- (b)V = Q/(4πε₀r) = 8.99 × 10⁹ × 6.0 × 10⁻⁹/0.050 ✓ = 1.1 × 10³ V ✓
- (c)E = Q/(4πε₀r²) = 8.99 × 10⁹ × 6.0 × 10⁻⁹/(0.050)² ✓ = 2.2 × 10⁴ V m⁻¹ ✓
- (d)E = −dV/dr; in magnitude E = V/r for a point charge: 2.16 × 10⁴ × 0.050 = 1.1 × 10³ V = V ✓✓
- (e)V at 10 cm = 539 V; ΔV = 539 − 1079 = −540 V ✓; W = qΔV = 2.0 × 10⁻⁹ × (−540) ✓ = −1.1 × 10⁻⁶ J (the field does the work as the like charge moves away) ✓
- (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.
The electric potential at a point is:
- Athe work done per unit positive charge bringing it from infinity
- Bthe force per unit charge
- Cthe field per unit distance
- Dthe charge per unit volume
The potential of a point charge varies with distance as:
- A1 / r
- B1 / r²
- Cr
- Dr²
The electric field is related to the potential by:
- AE = −dV/dr (the negative gradient)
- BE = V / r always
- CE = +dV/dr
- DE = V × r
The work done moving a charge q through a potential difference ΔV is:
- AqΔV
- BΔV / q
- Cq / ΔV
- DqΔV²
Quiz key
Potential is the work done per unit positive charge in moving it from infinity to the point.
V = Q / (4πε₀r), so V ∝ 1/r, falling off more gently than the field.
The field is the negative gradient of the potential: it points from high to low potential.
Work done = charge × potential difference = qΔV.
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.