Coulomb’s Law Class 12 Physics Numericals with Answers – CBSE Exam Practice

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Last Updated on April 11, 2025 by XAM CONTENT

Welcome to the Numerical Problem Series for Class 12 Physics! In this post, we focus on one of the most fundamental topics of electrostatics — Coulomb’s Law.

Here, you’ll find 10 well-crafted numerical problems, ranging from moderate to tough difficulty. These questions are suitable for CBSE board exams, JEE, and NEET aspirants.

What is Coulomb’s Law?

Coulomb’s Law states that:

$$
F=\frac{1}{4 \pi \varepsilon_0} \cdot \frac{\left|q_1 q_2\right|}{r^2}
$$

where:
– $F$ is the electrostatic force between two charges
– $q_1$ and $q_2$ are the magnitudes of the charges
– $r$ is the distance between the charges
– $\varepsilon_0$ is the vacuum permittivity

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Numericals on Coulomb’s Law Class 12 Physics

Numerical Problems

Each question below is designed to build your concept clarity.

Q1. Two charges of +3 μC and −5 μC are placed 20 cm apart in vacuum.
Find the magnitude and direction of the force on each charge. Also state whether the force is attractive or repulsive.

Q2. Two point charges q₁ and q₂ exert a force of 4 N on each other when placed 0.2 m apart in air. What will be the force between them if the separation is increased to 0.4 m?

Q3. Three charges are placed at the corners of an equilateral triangle of side \( 0.5\,\text{m} \):
\( q_A = +4\,\mu\text{C} \), \( q_B = -2\,\mu\text{C} \), \( q_C = +1\,\mu\text{C} \).
Calculate the net force on charge at A due to the other two.

Q4. Two charges of equal magnitude 1 μC but opposite signs are placed 1 m apart.
Find the electric force experienced by a third charge of +2 μC placed at the midpoint between them.

Q5. Two small spheres of mass 10 g each are suspended from a common point by silk threads of length 0.5 m. They repel each other due to similar charges and come to equilibrium with a separation of 0.1 m between them. Calculate the charge on each sphere.

(Assume angle is small so that tan θ ≈ sin θ)

Q6. Charges +3 μC and −6 μC are fixed at (0, 0) and (0.5 m, 0) respectively.
Find the point(s) on the x-axis where the net electrostatic force on a test charge would be zero.

Q7. The force between two point charges placed in air is 9 N.
If a dielectric slab of dielectric constant 3 is introduced between them, calculate the new force.

Q8. Two point charges +4 μC and +9 μC are placed 1 m apart.
Find the point along the line joining them where the net electric force on a test charge would be zero.

Q9. Two identical conducting spheres having charges +6 μC and −2 μC respectively are brought in contact and then separated by a distance of 50 cm. Calculate the final force between them.

Q10. Three charges each of +2 μC are placed at the corners of a right-angled triangle ABC with AB = 3 cm, BC = 4 cm.
Find the net force acting on the charge at vertex A due to the other two charges.

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Answers

Q1. 3.375 N, Attractive
Q2. 1 N
Q3. Approximately 0.259 N, direction downward (approx.)
Q4. 0 N
Q5. Approximately 29.7 μC
Q6. Approximately 0.207 m from origin
Q7. 3 N
Q8. 0.4 m from the +4 μC charge
Q9. 0.144 N, Repulsive
Q10. Approximately 0.4 N

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❌ Common Mistakes Students Make

Even though Coulomb’s Law seems straightforward, many students lose marks due to small but critical mistakes. Here are some of the most frequent ones:

⚠️ 1. Forgetting to Convert Units

Students often forget to convert microcoulombs (μC) to coulombs (C).

Tip: Always convert using:
1 μC = 1 × 10⁻⁶ C

⚠️ 2. Misusing the Signs of Charges

Students sometimes ignore whether charges are positive or negative.

Tip: Remember:

• Like charges → Repel
• Unlike charges → Attract
  Use signs only when determining direction, not in the magnitude formula.

⚠️ 3. Wrong Use of the Distance (r)

For Coulomb’s Law, the distance should be in meters and measured between centers of point charges.

Common Mistake: Using centimeters without converting to meters
Conversion: 1 cm = 0.01 m

⚠️ 4. Plugging in Incorrect Value of Constant (k)

Some students wrongly use the value of k or forget to square the distance.

Correct value of k:
k = 9 × 10⁹ Nm²/C²

⚠️ 5. Ignoring the Vector Nature in Multi-Charge Problems

In problems involving 3 or more charges, students add forces algebraically instead of using vector resolution.

Tip: Resolve each force into horizontal (Fx) and vertical (Fy) components. Use:
Fx = F × cos(θ)
Fy = F × sin(θ)
Then apply:
F_net = √(Fx² + Fy²)

⚠️ 6. Not Squaring Distance in Denominator

Students often plug in the distance directly into the formula without squaring it.

Correct formula:
F = k × (q₁ × q₂) / r²

Make sure to square the distance (r²).

⚠️ 7. Not Stating the Nature of the Force

Many students forget to mention whether the force is attractive or repulsive — a key part of the final answer, especially in exams.

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✅ Pro Tip:

Always follow this format while solving:

• Write the Given values
• Write the Formula
• Plug in the Calculation clearly
• Box the Final Answer with correct unit and nature of force

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Also check

• Coulomb’s Law Class 12 Physics Numericals with Answers – CBSE Exam Practice
• Refraction Through a Lens Class 12 Physics Numerical with Answers
• Electric Potential Class 12 Physics Numerical with Answers
• Superposition Principle of Electric Forces Class 12 Physics Numerical with Answers

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Frequently Asked Questions (FAQs) on Coulomb’s Law Class 12 Physics Numericals