Coulomb's law numericals: Class 12 practice
The force between two point charges is F = k q₁q₂ / r², with k = 9 × 10⁹ N m² C⁻². Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Scientific notation
The idea behind coulomb's law numericals
The force between two point charges is F = k q₁q₂ / r², with k = 9 × 10⁹ N m² C⁻². Like charges repel, unlike attract. Doubling r reduces F to one quarter.
Step-by-step method
- Convert μC to C (×10⁻⁶) and cm to m.
- F = 9 × 10⁹ × q₁q₂ / r².
- State attraction or repulsion.
- For ratio questions, use F ∝ 1/r².
Worked example 1 (Basic)
Find the force between charges of 9 μC and 1 μC placed 30 cm apart in vacuum.
- q₁ = 9 × 10⁻⁶ C, q₂ = 1 × 10⁻⁶ C, r = 0.3 m
- F = 9 × 10⁹ × 9 × 10⁻¹² / 0.0900
- F = 0.90 N, repulsive
- Answer: 0.90 N (repulsive)
Worked example 2 (Standard)
Find the force between charges of 1 μC and -5 μC placed 20 cm apart in vacuum.
- q₁ = 1 × 10⁻⁶ C, q₂ = -5 × 10⁻⁶ C, r = 0.2 m
- F = 9 × 10⁹ × 5 × 10⁻¹² / 0.0400
- F = 1.12 N, attractive
- Answer: 1.12 N (attractive)
Worked example 3 (Challenge)
Two charges repel with a force of 56.70 N at 10 cm. What is the force when the separation becomes 40 cm?
- F ∝ 1/r²
- New F = 56.70 ÷ 16 = 3.544 N
- Answer: 3.544 N
Common mistakes and misconceptions
- Not squaring r
- Leaving charges in μC
Practice questions
- (Basic) Find the force between charges of 1 μC and 5 μC placed 50 cm apart in vacuum.
- (Basic) Find the force between charges of 7 μC and 4 μC placed 30 cm apart in vacuum.
- (Standard) Find the force between charges of 1 μC and -2 μC placed 50 cm apart in vacuum.
- (Standard) Find the force between charges of 9 μC and -5 μC placed 20 cm apart in vacuum.
- (Challenge) Two charges repel with a force of 0.07 N at 50 cm. What is the force when the separation becomes 100 cm?
- (Challenge) Two charges repel with a force of 0.40 N at 30 cm. What is the force when the separation becomes 120 cm?
Answer key with full working
- Q1: q₁ = 1 × 10⁻⁶ C, q₂ = 5 × 10⁻⁶ C, r = 0.5 m → F = 9 × 10⁹ × 5 × 10⁻¹² / 0.2500 → F = 0.18 N, repulsive → Answer: 0.18 N (repulsive)
- Q2: q₁ = 7 × 10⁻⁶ C, q₂ = 4 × 10⁻⁶ C, r = 0.3 m → F = 9 × 10⁹ × 28 × 10⁻¹² / 0.0900 → F = 2.80 N, repulsive → Answer: 2.80 N (repulsive)
- Q3: q₁ = 1 × 10⁻⁶ C, q₂ = -2 × 10⁻⁶ C, r = 0.5 m → F = 9 × 10⁹ × 2 × 10⁻¹² / 0.2500 → F = 0.07 N, attractive → Answer: 0.07 N (attractive)
- Q4: q₁ = 9 × 10⁻⁶ C, q₂ = -5 × 10⁻⁶ C, r = 0.2 m → F = 9 × 10⁹ × 45 × 10⁻¹² / 0.0400 → F = 10.12 N, attractive → Answer: 10.12 N (attractive)
- Q5: F ∝ 1/r² → New F = 0.07 ÷ 4 = 0.018 N → Answer: 0.018 N
- Q6: F ∝ 1/r² → New F = 0.40 ÷ 16 = 0.025 N → Answer: 0.025 N
Syllabus note
This skill is listed under "Electric Charges and Fields" for Class 12 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is coulomb's law numericals in?
"Electric Charges and Fields", Class 12 Physics (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.