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Coulomb’s Law - Coulomb's Law (Scalar Form): Force Between Two Point-Charges

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Estimated time: 10 minutes
CISCE: Class 12

Introduction

Coulomb's Law is the foundational quantitative law of electrostatics. It describes the force of attraction or repulsion between two stationary, electrically charged point objects, playing the same role in electrostatics that Newton's Law of Gravitation plays in mechanics.

Every electric field, potential, and capacitance concept in this chapter builds on Coulomb's Law. Mastering it is essential before moving to Electric Field and Gauss's Law.

CISCE: Class 12

Key Terms (Glossary)

Term Meaning
Point charge A charge whose physical size is negligible compared to the distance between charges
Electrostatic force The force of attraction/repulsion between charges at rest
Permittivity (ε) A measure of how much a medium resists the electric field between charges
Permittivity of free space (ε0) Permittivity of vacuum; ε0 = 8.854 × 10-12 C2/(N·m2)
Relative permittivity / Dielectric constant (K) Ratio K = ε/ε0; indicates how much a medium reduces the force compared to vacuum
Coulomb's constant (k) k = 1/(4πε0) ≈ 9 × 109 N·m2/C2 in vacuum/air
CISCE: Class 12

Law: Coulomb's Law (Scalar Form)

Coulomb's Law: The electrostatic force of interaction between two stationary point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. The force acts along the straight line joining the two charges.

Derivation (Step-by-Step)

Step 1: Force is directly proportional to the product of charge magnitudes:

F ∝ q1q2

Step 2: Force is inversely proportional to the square of the separation distance:

F ∝ \[\frac {1}{r^2}\]

Step 3: Combining Steps 1 and 2:

F ∝ \[\frac {q_1q_2}{r^2}\]

Step 4: Introducing the proportionality constant k:

F = k ⋅ \[\frac {q_1q_2}{r^2}\]

where k = 1/(4πε0) ≈ 9 × 109 N·m2/C2 (in vacuum/air)

CISCE: Class 12

Effect of the Medium

When charges are placed in a dielectric medium instead of vacuum, the force reduces:

\[F_{medium}=\frac{1}{4\pi\varepsilon}\frac{q_1q_2}{r^2}=\frac{F_{vacuum}}{K}\]

Medium Dielectric constant (K)
Vacuum 1
Air ≈ 1
Water ≈ 80
Glass 5 – 10
CISCE: Class 12

Coulomb's Law vs. Newton's Law of Gravitation

Feature Coulomb's Law Newton's Law of Gravitation
Formula F = kq1q2/r2 F = Gm1m2/r2
Constant k ≈ 9 × 109 N·m2/C2 G ≈ 6.67 × 10-11 N·m2/kg2
Nature of force Attractive or repulsive Always attractive
Medium dependence Depends on medium (ε) Independent of medium
Applies to Point charges Point masses
CISCE: Class 12

Real-Life Analogy

Think of Coulomb's Law like two magnets sensing distance: the closer they are, the stronger the pull or push — but because the effect weakens with the square of distance, doubling the gap cuts the force to a quarter, not just half. A practical example: static cling between a balloon and hair after rubbing demonstrates the attractive form of this law.

Video Tutorials

We have provided more than 1 series of video tutorials for some topics to help you get a better understanding of the topic.

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Shaalaa.com | Electrostatics Coulomb's Law part-1

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Electrostatics Coulomb's Law part-1 [00:56:07]
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Electrostatics Coulomb's Law part-1
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coulombs Force part-2
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coulombs law and charge numericals
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Related QuestionsVIEW ALL [80]

Two identical pith balls, each carrying a charge q, are suspended from a common point by two strings of equal length l. Find the mass of each ball if the angle between the strings is 2θ in equilibrium. 

Suppose an attractive nuclear force acts between two protons which may be written as F=Ce−kr/r2. Write down the dimensional formulae and appropriate SI units of C and k.   

Four equal charges q are placed at the four comers A, B, C, D of a square of length a. The magnitude of the force on the charge at B will be ______.

Two particles of masses 5.0 g each and opposite charges of +4.0 × 10−5 C and −4.0 × 10−5 C are released from rest with a separation of 1.0 m between them. Find the speeds of the particles when the separation is reduced to 50 cm.  

Two insulating small spheres are rubbed against each other and placed 1 cm apart. If they attract each other with a force of 0.1 N, how many electrons were transferred from one sphere to the other during rubbing?

Three-point charges q, – 4q and 2q are placed at the vertices of an equilateral triangle ABC of side 'l' as shown in the figure. Obtain the expression for the magnitude of the resultant electric force acting on the charge q

(b) Find out the amount of the work done to separate the charges at infinite distance.

Two charged particles, with equal charges of 2.0 × 10−5 C, are brought from infinity to within a separation of 10 cm. Find the increase in the electric potential energy during the process 

Find the ratio of the electrical and gravitational forces between two protons.

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