18.2Electrostatics
Electric Force and Coulomb’s Law — American System Physics Revision Notes & Topical Questions
10 min read 7 parts Lesson 4 of 5 1 quiz
Lesson summary
State Coulomb's law and identify the variables and their units.Coulomb's lawforce = Coulomb constant × charge 1 × charge 2 ÷ distance², F = kq1q2/r2 (N; C; m).What the symbols mean: F = electric force (N) · Q1, Q2 = charges (C) · r = separation (m) · k = 1/4πε0 = 8.99 × 109 N m2 …
- Inverse square
- Newton's second law still applies
- The sign of the product tells the direction
- Electric (electrostatic) force
- Coulomb constant (k)
- Permittivity of free space (ε0)
Section 1 of 7Electric Force and Coulomb’s Law
1
2
Charles Coulomb measured electric forces with a torsion balance, finding force depends on each charge and on the square of the distance.
3
Coulomb's law applies to point charges and to uniformly charged spheres, measured centre to centre.
4The sign of the product tells the direction
The sign of the product tells the direction positive means repulsion, negative means attraction. It is usually safest to calculate with magnitudes, then decide direction from the charges.
5
Because k is enormous, even microcoulomb charges a few centimetres apart produce forces of several newtons; everyday static charges are typically nanocoulombs to microcoulombs.
6
Both charges experience the same size of force, even if one charge is much bigger. The smaller-mass object has the larger acceleration.
7
For several charges, forces combine by vector addition. In a line, add with signs; at right angles, use Pythagoras for the size and trigonometry for the direction.
8
Electric forces hold atoms and molecules together, and cause friction, tension and normal (contact) forces at the atomic level.
9
Gravity dominates on large scales because large objects are almost exactly neutral, whereas mass is always positive and adds up.
10
A charged pith ball hanging on a thread near another charge comes to rest where tension, weight and electric force balance; this allows charge to be calculated.
Section 2 of 7Process & sequence
1
Identify the two charges and convert to coulombs (μC × 10−6, nC × 10−9).
2
Find the separation r in metres (centre to centre).
3
Substitute magnitudes into F = k|q1q2|/r2 and square r carefully.
4
Decide the direction: like charges repel, unlike attract.
5
For three or more charges, find each force separately and add them as vectors (components if not in a line).
6
Quote the answer in newtons with a direction and 2–3 significant figures.
Solving a Coulomb's law problemwrite these steps in this order; each step is a marking point.
1
Convert all charges to C and distances to m.
2
Calculate the force magnitude with F = k|q₁q₂|/r².
3
Decide the direction from the signs (like repel, unlike attract).
4
Repeat for each other charge acting on the chosen charge.
5
Add the forces as vectors to find the net force and state its direction.
Section 3 of 7Compare
| Feature | Electric force | Gravitational force |
|---|---|---|
| Depends on | Charge | Mass |
| Law | F = kq1q2/r2 | F = Gm1m2/r2 |
| Constant | k = 8.99 × 109 N m2/C2 | G = 6.67 × 10−11 N m2/kg2 |
| Direction | Attract or repel | Attract only |
| Relative strength (two protons) | About 1036 times larger | Tiny |
| Distance dependence | Inverse square | Inverse square |
| Change | New force |
|---|---|
| Double one charge | 2F |
| Double both charges | 4F |
| Double distance | F/4 |
| Halve distance | 4F |
| Triple distance | F/9 |
Section 4 of 7Worked examples
3.4 N
Two point charges of +3.0 μC and −5.0 μC are 0.20 m apart. Find the size and nature of the force.
- F = kq1q2/r2 = 8.99 × 109 × 3.0 × 10−6 × 5.0 × 10−6 / (0.20)2 = 0.1349/0.040 = 3.4 N, attractive (unlike charges).
2.7 N
Two charges repel with a force of 12 N. The distance between them is tripled and one charge is doubled. Find the new force.
- Fnew = F × 2 / 32 = 12 × 2/9 = 2.7 N (repulsive).
Charges A (+2.0 μC) at x = 0, B (+2.0 μC) at x = 0.10 m, and C (−1.0 μC) at x = 0.30 m. Find the net force on B.
- A on B: F = 8.99 × 109 × (2.0 × 10−6)2/(0.10)2 = 3.6 N, repulsive, so +x direction.
- C on B: F = 8.99 × 109 × 2.0 × 10−6 × 1.0 × 10−6/(0.20)2 = 0.45 N, attractive towards C, also +x.
- Net3.6 + 0.45 = 4.0 N in the +x direction.
Section 5 of 7Key terms
Section 6 of 7Command terms
Command terms
Identify / Describe (FRQ)
A short, specific statement; describing requires relevant characteristics, not a single word.
Explain / Justify (FRQ)
Give the cause-and-effect reasoning or evidence; a restated fact does not score.
Calculate
Show setup, substitution and the answer with units.
Predict
State the expected outcome; add a reason only if asked to justify.
MCQ technique
Read every option; eliminate distractors that are true statements but do not answer the question; watch for NOT/EXCEPT.
Section 7 of 7Exam technique
Keywords the mark scheme looks for in this lesson
Keywords the mark scheme looks for in this lesson
Electric (electrostatic) force · Coulomb's law · Coulomb constant (k) · Permittivity of free space (ε0) · Point charge · Inverse-square law · Separation (r) · Action–reaction pair · Net electric force · Attractive force · Repulsive force
Learn each definition in the Key words tab exactly; a missing keyword in a definition usually loses the mark.
How to get full marks (examiner guidance)
1
Answer exactly what is asked; extra correct material does not earn credit, and contradictory statements can cancel credit (AP FRQ).
2
Use precise vocabulary, never “it/stuff/things”.
3
Show units and working in calculations.
4
In MCQs, predict the answer before reading the options, then eliminate.
Words to avoid
1
F is inversely proportional to distanceF is inversely proportional to the square of the distance.
2
the bigger charge feels a bigger forceboth charges feel equal and opposite forces (Newton's third law).
3
r is the distance between the surfacesr is the distance between the centres of the charges.
4
forgetting μconvert μC to C by multiplying by 10⁻⁶ before substituting.
5
a negative force means a smaller forcea negative product means the force is attractive.
Instant feedbackCheck yourself
Q1. If the distance between two charges is doubled, the force becomes
- A. 2F
- B. F/2
- C. F/4
- D. 4F
Show answer
C. Inverse square: (1/2)² = 1/4.
Q2. The SI unit of k in Coulomb's law is
- A. N m²/C²
- B. C²/N m²
- C. N/C
- D. J/C
Show answer
A. k = Fr²/(q₁q₂) has units N m²/C².
Q3. Two charges of 1.0 μC are 1.0 m apart. The force is about
- A. 9.0 × 10⁻³ N
- B. 9.0 N
- C. 9.0 × 10⁻⁶ N
- D. 1.0 N
Show answer
A. F = 9.0×10⁹ × 1.0×10⁻¹² / 1 = 9.0×10⁻³ N.
Q4. A +4 μC charge and a +1 μC charge exert forces on each other. The force on the +1 μC charge is
- A. 4 times larger
- B. equal in size
- C. 4 times smaller
- D. zero
Show answer
B. Newton's third law: equal and opposite.
Q5. Both charges are tripled at the same distance. The force
- A. triples
- B. increases 6 times
- C. increases 9 times
- D. is unchanged
Show answer
C. F ∝ q₁q₂: 3 × 3 = 9.
Q6. A +2 C and −2 C charge placed near each other will
- A. repel
- B. attract
- C. not interact
- D. both become positive
Show answer
B. Unlike charges attract.
Marked practiceQuizzes for this lesson
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