Electric Charges and Fields
The fundamental force that binds atoms, powers circuits, and holds the universe together
Table of Contents
1.1 Introduction
All of us have the experience of seeing a spark or hearing a crackle when we take off our synthetic clothes or sweater, particularly in dry weather. Another common example of electric discharge is lightning during thunderstorms. The study of electric charges at rest (electrostatics) forms the foundation for understanding electricity, magnetism, and all of electromagnetic theory.
1.2 Electric Charge
Electric charge is a fundamental property of matter. Like masses, it is a scalar quantity but unlike mass, charges come in two types: positive and negative. Like charges repel, unlike charges attract.
Quantization of Charge
Charge always exists in integer multiples of elementary charge e = 1.6 × 10⁻¹⁹ C. q = ne where n is an integer.
Conservation of Charge
Total charge in an isolated system remains constant. Charge can be transferred but not created or destroyed.
1.3 Conductors and Insulators
Materials that allow electric charge to flow freely are called conductors (metals, human body, earth). Materials that do not allow charge flow are insulators (glass, rubber, plastic).
1.4 Charging by Induction
A neutral conductor can be charged without direct contact. When a charged body is brought near a neutral conductor, charges redistribute — this is charging by induction. The near side gets opposite charge, far side gets same charge.
1.5 Coulomb's Law
The force between two point charges is directly proportional to the product of charges and inversely proportional to the square of the distance between them:
The net force on a charge due to multiple charges is the vector sum of individual forces. Each pair interacts independently — the presence of other charges doesn't affect the force between any pair.
1.6 Electric Field
The electric field at a point is the force per unit positive test charge placed at that point. It is a vector field that exists in space around charges.
Electric field lines: start from positive charges, end on negative charges, never cross, and are denser where field is stronger.
1.7 Electric Flux
Electric flux is the measure of the number of electric field lines passing through a surface:
1.8 Gauss's Law
Gauss's law relates the total electric flux through a closed surface to the charge enclosed:
Sphere
E = kq/r² outside, E = 0 inside. Shell theorem: outside behaves as if all charge at center.
Infinite Plane Sheet
E = σ/(2ε₀) — uniform field, independent of distance. σ = surface charge density.
Infinite Line Charge
E = λ/(2πε₀r) — decreases as 1/r. λ = linear charge density.
Conducting Shell
Field inside = 0. All charge resides on outer surface. Used in Faraday cage shielding.