Coulomb’s Law Study Pack

Kibin's free study pack on Coulomb’s Law includes a 3-section study guide, 8 quiz questions, 10 flashcards, and 1 open-ended Explain review question. Sign up free to track your progress toward mastery, plus upload your own notes and recordings to create personalized study packs organized by course.

Last updated May 21, 2026

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Coulomb’s Law Study Guide

Master the mathematics and physical reasoning behind electrostatic interactions with this study pack on Coulomb's Law. Work through the force equation F = k|q₁q₂|/r², explore how attraction and repulsion depend on charge signs, and understand the inverse-square relationship that governs distance effects. Superposition, point charge assumptions, and electric field connections are all covered.

Key Takeaways

  • •Coulomb's Law states that the electrostatic force between two point charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance separating them.
  • •The mathematical form is F = k|q₁q₂|/r², where k is Coulomb's constant (approximately 8.99 × 10⁹ N·m²/C²), q₁ and q₂ are the charge magnitudes, and r is the separation distance.
  • •The force is attractive when the two charges have opposite signs and repulsive when they share the same sign, and it acts along the line connecting the two charges.
  • •Because force depends on 1/r², doubling the distance reduces the force to one-quarter of its original value — a hallmark of inverse-square relationships.
  • •Coulomb's Law applies strictly to point charges or spherically symmetric charge distributions, and multiple charges are handled by applying the superposition principle to sum all pairwise force vectors.
  • •The electrostatic force is transmitted through the electric field: each charge creates a field in surrounding space, and the other charge experiences a force by interacting with that field.

Electric Charge: The Foundation of Electrostatic Force

Before Coulomb's Law can be applied, it is essential to understand the property that drives electrostatic interactions — electric charge — including how it is measured, conserved, and categorized.

Nature and Sign of Electric Charge

  • •Electric charge is an intrinsic property of matter carried by subatomic particles: protons carry positive charge (+e) and electrons carry negative charge (−e), where e = 1.602 × 10⁻¹⁹ C (the elementary charge).
  • •Charge comes in two polarities — positive and negative — and objects become charged when electrons are transferred between them, leaving a net surplus or deficit.
  • •Like charges (both positive or both negative) repel each other; unlike charges (one positive, one negative) attract each other.

Conservation and Quantization of Charge

  • •The law of conservation of charge states that the total electric charge in an isolated system never changes; charge can be redistributed but not created or destroyed.
  • •Charge is also quantized, meaning any measurable charge is an integer multiple of the elementary charge e — you cannot have half an electron's worth of charge in isolation.

The Coulomb as the SI Unit

  • •Charge is measured in coulombs (C); one coulomb is the amount of charge transported by a current of one ampere in one second.
  • •A single proton or electron carries roughly 1.6 × 10⁻¹⁹ C, so even a small charged object at the macroscopic scale involves enormous numbers of elementary charges.

Coulomb's Law: The Mathematical Relationship

Coulomb's Law provides a precise, quantitative description of the force between two stationary point charges, relating force magnitude to charge sizes and the distance between them.

The Coulomb's Law Equation

  • •The magnitude of the electrostatic force is given by F = k|q₁q₂|/r², where F is force in newtons (N), q₁ and q₂ are the charges in coulombs, and r is the distance between them in meters.
  • •Coulomb's constant k ≈ 8.99 × 10⁹ N·m²/C² sets the scale of electrostatic interactions in SI units; it can also be written as k = 1/(4πε₀), where ε₀ ≈ 8.85 × 10⁻¹² C²/(N·m²) is the permittivity of free space.
  • •The absolute value signs around the charge product ensure the formula yields a positive force magnitude; the direction (attractive or repulsive) is determined separately from the signs of q₁ and q₂.

The Inverse-Square Dependence on Distance

  • •Because force varies as 1/r², halving the separation between charges quadruples the force, while tripling the distance reduces the force to one-ninth its original value.
  • •This inverse-square relationship is structurally identical to Newton's Law of Universal Gravitation, which similarly falls off with the square of distance — though electrostatic forces can be either attractive or repulsive, while gravity is exclusively attractive.

Directionality of the Electrostatic Force

  • •Coulomb's Law is a vector law: the force on each charge acts along the straight line connecting the two charges.
  • •When charges are opposite in sign, the force vectors on each charge point toward the other charge (attraction); when charges share the same sign, the force vectors point away from each other (repulsion).
  • •Newton's third law applies — the force that q₁ exerts on q₂ is equal in magnitude and opposite in direction to the force q₂ exerts on q₁.

About this Study Pack

Created by Kibin to help students review key concepts, prepare for exams, and study more effectively. This Study Pack was checked for accuracy and curriculum alignment using authoritative educational sources. See sources below.

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