Lesson 6.1 • Competency 6.1Complete Lesson

Coulomb’s Law and Electric Field Intensity

Quantization and conservation of electric charge, Coulomb’s Law in vacuum and dielectric media, permittivity, electric field strength E = F/q = Q/(4πεr²), electric dipoles, and field line properties.

Marking a lesson complete represents finishing your study of the topic; it does not denote tested mastery.

Learning Objectives

State Coulomb’s Law (F = (1/4πε₀εᵣ) (q₁q₂/r²)) and calculate electrostatic forces between multiple point charges in vacuum and dielectric media.
Define electric field intensity E = F/q₀ and determine the resultant field due to systems of point charges and electric dipoles using vector addition.
Sketch and interpret electric field line patterns for isolated point charges, dipoles, and pairs of like charges, stating physical boundary rules.

Core Theory & Concepts

Electrostatics studies electric charges at rest. Two fundamental principles govern all electrostatic interactions: charge conservation (total charge in an isolated system remains strictly constant) and Coulomb’s inverse-square law, which quantifies the mutual forces between stationary charges.

Coulomb’s Law

Mutual force between two point charges: F = (1 / 4πε) (|q₁ q₂| / r²), where 1/(4πε₀) ≈ 8.99 × 10⁹ N m² C⁻² in vacuum.

F = \frac{1}{4\pi \varepsilon_0 \varepsilon_r} \frac{|q_1 q_2|}{r^2}

Electric Field Intensity

The electrostatic force per unit positive test charge: E = F / q₀ = (1 / 4πε) (Q / r²). Radially outward from positive charge, inward toward negative charge.

E = \frac{1}{4\pi \varepsilon_0 \varepsilon_r} \frac{Q}{r^2}

Relative Permittivity (Dielectric Constant)

The ratio of force in vacuum to force in a medium: εᵣ = F_vacuum / F_medium = ε / ε₀. For air/vacuum εᵣ ≈ 1; for water εᵣ ≈ 80.

\varepsilon_r = \frac{\varepsilon}{\varepsilon_0} = \frac{F_{\text{vacuum}}}{F_{\text{medium}}}

Common Misconceptions

Misconception

Electric field lines represent actual physical trajectories that a released charged particle will always follow.

Physical Clarification:Field lines only indicate the direction of the electrostatic force at each instantaneous point (acceleration direction). Because a moving particle possesses inertia, its actual velocity trajectory generally diverges from curved field lines.

Syllabus Topic Outline

Competency 6.1

1Charge quantization (q = ne) and charge conservation principles
2Coulomb’s Inverse Square Law and permittivity of media (ε = ε₀ εᵣ)
3Electric field intensity definition: E = F / q₀ (N C⁻¹ or V m⁻¹)
4Superposition principle for electric fields and neutral points
5Electric dipoles, dipole moment (p = 2aq), and axial vs equatorial fields
6Properties and rules of electric field lines