Electric fields: force, potential and capacitors
Key idea: Keep vector force and field distinct from scalar potential and energy, then use the negative potential gradient, uniform fields and capacitor graphs with explicit signs and assumptions.
Before you start: Energy & Fields objective chainMotion & Forces objective chain
By the end, you can
- Apply Coulomb's law and the point-charge field equation with correct inverse-square scaling and direction.
- Define and calculate electric potential and two-charge potential energy, then use the negative potential gradient.
- Analyse force, acceleration and trajectory in a uniform electric field.
- Define capacitance and obtain stored-energy equations from the area under a potential-difference–charge graph.
Starting-point self-check
1. Check your starting point
Attempt all five groups without notes and mark the first inverse-square, sign, scalar/vector, gradient or graph-area decision you cannot justify. Use the recorded topic diagnostic above when you want scoring and a personalised repair plan.
Coulomb force between point charges 14(a)
Question 1
Charges +3.0 μC and −2.0 μC are 0.40 m apart in air. Find the force magnitude and direction using 1/(4πε₀) = 8.99 × 10⁹ N m² C⁻².
Check the model response
F = k|Q₁Q₂|/r² = 0.337 N. Opposite charges attract, so each force is directed towards the other charge; the two forces form an equal-and-opposite pair.
repair
2. Repair the common breaks
Use only the correction matching an error, then retry the corresponding diagnostic.
Coulomb force between point charges 14(a)
Check this idea
Misconception: Coulomb force is inversely proportional to separation.
Repair: For point charges it is inversely proportional to separation squared.
Check this idea
Misconception: The sign of the formula is enough to describe both force directions.
Repair: Calculate the magnitude, then use charge signs and the joining line to state attraction or repulsion and each vector direction.
worked example
3. Follow five worked models
Follow how each solution fixes the source geometry, vector direction, potential reference, field uniformity or graph axes before calculating.
Coulomb force between point charges 14(a)
Model 1
Two identical +5.0 nC charges repel with 2.25 × 10⁻⁵ N. Find their separation.
Check the model response
From F = kQ²/r², r = √(kQ²/F) = √[(8.99 × 10⁹)(5.0 × 10⁻⁹)²/(2.25 × 10⁻⁵)] = 0.100 m. The positive sign determines repulsion, not the magnitude calculation.
guided practice
4. Guided practice
Use each hint only to select the inverse-square relation, sign convention, gradient, force direction or energy form.
Coulomb force between point charges 14(a)
Question 1
A separation triples while both point charges stay fixed. State the force factor.
Hint: Apply the inverse square to the separation factor, not just its reciprocal.
Check the model response
F ∝ 1/r², so the force becomes 1/3² = 1/9 of its original magnitude.
independent practice
5. Independent practice
Solve without repair notes and state every point-charge, free-space, uniform-field and non-relativistic assumption used.
Coulomb force between point charges 14(a)
Question 1
Explain all conditions in the syllabus form of Coulomb’s law and solve for the force between +1.5 μC and +4.0 μC separated by 0.25 m.
Check the model response
The charges are treated as points in free space or air, with separation measured centre-to-centre. F = (8.99 × 10⁹)(1.5 × 10⁻⁶)(4.0 × 10⁻⁶)/(0.25)² = 0.863 N, repulsive.
Practice exit check
6. Practice assessment
Use this as extra closed-book practice, then complete the separate recorded assessment in your plan.
Coulomb force between point charges 14(a)
Question 1
Two point charges −2.0 nC and −8.0 nC are 0.60 m apart in air. Calculate and describe the force.
Check the model response
F = (8.99 × 10⁹)(2.0 × 10⁻⁹)(8.0 × 10⁻⁹)/(0.60)² = 4.00 × 10⁻⁷ N. Like charges repel along their joining line.
Re-test practice
7. Delayed re-test practice
Return after at least three days and solve these fresh contexts without reopening earlier responses. The recorded plan enforces the delay and uses a separate re-test family for selected-response skill-group evidence.
Coulomb force between point charges 14(a)
Question 1
If one charge doubles and separation halves, state the Coulomb-force factor.
Check the model response
F ∝ Q₁Q₂/r², so doubling one charge gives ×2 and halving r gives ×4: the total factor is ×8.