How to Derive and Apply Coulomb’s Law in Physics Problems
Coulomb’s law is a cornerstone of electrostatics, describing how electric charges interact through force. It shows that the force between two point charges depends on their charge values and the distance separating them. This concept is vital for JEE Main, as it underpins topics from basic charge interactions to advanced concepts like electric fields. Every student must be comfortable with applying Coulomb’s law in scalar and vector forms, recognizing the influence of the medium, and avoiding common sign or direction mistakes. Mastering these basics provides a strong foundation for more complex topics such as electric potential, fields, electrostatic shielding, and capacitors.
What is Coulomb's Law? Statement and Intuitive Understanding
Coulomb’s law states that the electrostatic force between two stationary point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. It also states that the force acts along the line joining the charges and can be attractive or repulsive.
Charles-Augustin de Coulomb established this relationship in 1785 with precise experiments, which led to clear mathematical descriptions of electric force. If you have ever felt your hair stand when you remove a wool cap, you’ve witnessed Coulomb’s law in action due to separating and interacting charges.
Coulomb's Law Formula and Variables Explained
The scalar form of Coulomb’s law is:
F = k × |q1q2| / r2
- F = magnitude of electrostatic force (N)
- q1, q2 = charges (Coulombs, C)
- r = distance between charges (metres, m)
- k = Coulomb constant (9.0 × 109 N·m2·C-2)
The vector form accounts for direction:
→F = k × (q1q2 / r2) →r̂
Here, →r̂ is the unit vector from one charge to the other. The sign of the product q1q2 determines if the force is attractive (opposite charges) or repulsive (like charges).
| Variable | Physical Meaning | SI Unit |
|---|---|---|
| F | Electrostatic force | Newton (N) |
| q1, q2 | Point charges | Coulomb (C) |
| r | Separation between charges | Metre (m) |
| k | Coulomb constant (1/4πε0) | N·m2/C2 |
Coulomb's Law Derivation and Exam Applications
To derive Coulomb’s law, consider two small charged spheres suspended so their forces can be measured. Using a torsion balance (as Coulomb did), experiments reveal the force varies:
- Proportional to |q1q2| (if either charge doubles, force doubles)
- Inversely proportional to r2 (if separation doubles, force drops to one-fourth)
The modern derivation uses empirical laws and symmetry, concluding:
F ∝ (|q1q2|)/r2 ⇒ F = k·|q1q2|/r2
For JEE Main, always write the full law statement, then the formula. Draw two charges at a distance r and indicate the force’s direction for both same and opposite sign charges. Show the use of unit vectors when asked for vector form.
Units, Significance of k, and Influence of Medium
Numerical problems require correct SI units and the right value for k. Always check if the question involves air (vacuum) or another medium like water.
| Constant/Unit | Value | Used in |
|---|---|---|
| k (Coulomb constant) | 9 × 109 N·m2/C2 | Vacuum or air |
| ε0 (Permittivity of free space) | 8.85 × 10-12 C2·N-1·m-2 | Coulomb's law formula |
| Coulomb (C) | SI unit of charge | All charges (q1, q2) |
If charges are in a different medium, divide k by the relative permittivity (εr) of that medium.
Coulomb's law is conceptually similar to Newton's law of gravitation but applies to charges, not masses. The “Coulombic interaction” serves as the starting point for complex interactions in molecules, solids, and plasmas. For exam problems, writing units and constant values accurately is key. You can further reinforce your understanding with the electrostatics mock test or focused examples in electric field lines practice pages.
Coulomb's Law: Solved Example, Applications, and Pitfalls
Let’s quickly solve a typical exam problem. “Two point charges, +2 × 10-6 C and -3 × 10-6 C, are placed 0.2 m apart in air. Calculate the force between them.”
- q1 = +2 × 10-6 C
- q2 = -3 × 10-6 C
- r = 0.2 m
- k = 9 × 109 N·m2/C2
F = [9 × 109 × 2 × 10-6 × 3 × 10-6]/(0.2)2 = (9 × 2 × 3 × 109-6-6)/0.04
F = (54 × 10-3)/0.04 = 1.35 N (attractive, since the sign is negative).
- Always check the sign of charges to determine force direction.
- Convert all units to SI before calculation.
- For non-point charges or extended objects, Coulomb’s law must be applied to individual pairs, then summed (integration if continuous distributions).
- In water or other media, adjust using the medium's permittivity.
- If multiple charges act, use the superposition principle by adding forces as vectors.
- Don't forget the basics of electrostatics when approaching new types of problems.
Coulomb's law applies beyond school physics. It governs bonding in molecules, force between ions, and behavior of static electricity in daily life. It is foundational for topics like capacitors and capacitance and even semiconductor physics.
Common Mistakes and Quick Revision for Coulomb’s Law
- Assuming force is always repulsive—check charge signs first.
- Forgetting to use square of distance: do not use r instead of r2.
- Confusing F with electric field (E); use Coulomb's law for force calculations only.
- Using wrong value of k when charges are not in vacuum or air.
- Ignoring vector nature on multi-charge problems—forgetting direction matters.
- Not drawing clear force diagrams in derivations or answers.
- Overlooking the role of permittivity, especially in different media.
- Mixing up scalar and vector forms in answers; always match the question's requirement.
For fast revision, note the core essentials: law statement, formula (scalar and vector), SI units, effect of sign/distance, constant’s value, and symmetric use of force for pair charges. Revise using the electrostatics revision notes or relevant mock test questions to strengthen your grip.
- Coulomb's law gives force between point charges; F ∝ q1q2/r2.
- Like charges repel; unlike charges attract.
- Force acts along the line joining charges.
- SI unit of charge: Coulomb (C).
- Coulomb constant: 9 × 109 N·m2/C2.
- Adjust formula for different media using permittivity.
- Use superposition for three or more charges.
Coulomb's law forms the base for the entire subject of electrostatics. It explains real-life phenomena, from static cling to forces in atoms. Linking this law to Gauss's law, electric potential helps you progress through JEE Main Physics confidently. Vedantu’s resources are designed by expert educators to simplify every such concept and reinforce your preparation for success.
FAQs on Coulomb’s Law: Statement, Formula and Uses
1. What does Coulomb's law explain?
Coulomb's law explains the electrostatic force between two point charges. It states that the force of attraction or repulsion between two stationary electric charges is proportional to the product of their charges and inversely proportional to the square of the distance between them.
Key points:
- Describes interaction between electric charges
- Applicable for point charges in electrostatics
- Forms the foundation of electrostatics in physics
2. What is the statement of Coulomb's law for class 12?
The statement of Coulomb's law for Class 12 Physics is:
The magnitude of the electrostatic force (F) between two stationary point charges (q1 and q2), separated by a distance (r) in vacuum, is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Formula:
F = k × |q1q2| / r2
Where k is the Coulomb constant.
3. How do you derive Coulomb's law?
The derivation of Coulomb’s law is based on experimental observations made by Charles-Augustin de Coulomb using a torsion balance.
To derive:
- Consider two point charges, q1 and q2, separated by distance r.
- It is observed that force is proportional to each charge: F ∝ q1q2
- Force is inversely proportional to the square of distance: F ∝ 1/r2
- Combining proportionalities and introducing the constant k: F = k × |q1q2| / r2
4. What is the value and unit of the Coulomb constant?
The Coulomb constant (denoted as k) has a value of 8.9875 × 109 N m2 C-2 in SI units.
Key details:
- Unit: Newton metre squared per coulomb squared (N·m2·C-2)
- k = 1/(4πε0) where ε0 is the permittivity of free space
- Use this value for problems involving electric force calculations
5. How is Coulomb's law used in numerical problems?
In numerical problems, Coulomb's law helps you calculate the force between two charges. Follow these steps:
- Identify the charges q1 and q2, and the distance r between them
- Substitute values into the formula: F = k × |q1q2| / r2
- Include correct units for force (N), charges (C), and distance (m)
- Consider the sign for attraction or repulsion
6. Does Coulomb's law apply to non-point charges?
Coulomb’s law applies strictly to point charges, but can be extended to spherically symmetric charge distributions at distances much larger than their sizes.
Keep in mind:
- Use for point or very small charges
- For extended bodies, use integration or Gauss's law
- Exact form may not apply for irregular or large bodies
7. How does the medium (like air vs. water) affect the force?
The electrostatic force calculated by Coulomb’s law depends on the medium between the charges, as different materials have different permittivities.
Differences:
- In vacuum: Maximum force (k set for vacuum/permittivity of free space)
- In other media: Force is reduced (divide by the material's relative permittivity/ dielectric constant)
- In water or glass, the force is much less than in air or vacuum
8. What mistakes do students make when using the vector form?
Common mistakes in the vector form of Coulomb’s law include:
- Ignoring the direction of force (force acts along the line joining charges)
- Using the wrong signs for attraction (opposite charges) or repulsion (like charges)
- Mixing up unit vectors
- Forgetting to apply superposition principle with multiple charges
9. Are there exceptions where Coulomb's law fails?
Coulomb’s law may fail or be inaccurate in:
- Cases involving non-point charges at short distances
- Within conductors or at atomic/subatomic scales (quantum effects apply)
- When charges are moving rapidly (magnetic effects must be considered)
10. How does Coulomb’s law compare to Newton’s law of gravitation?
Both Coulomb’s law and Newton’s law of gravitation follow the inverse square law, but differ in physical meaning:
- Coulomb’s law: Acts between electric charges; force can be attractive or repulsive
- Newton’s law: Acts between masses; force is always attractive
- Magnitude: Electrostatic forces are generally much stronger than gravitational forces between elementary particles
11. What is the formula for Coulomb's law and how do you use it?
The formula for Coulomb's law is:
F = k × |q1q2| / r2
Where:
- F = electrostatic force (in Newtons)
- q1 and q2 = magnitudes of the charges (in Coulombs)
- r = distance separating the charges (in metres)
- k = Coulomb constant
