Electric Charges and Fields
A thorough exploration of electric charge, Coulomb's law, electric field, field lines, electric flux, electric dipoles, Gauss's law, and its applications to symmetric charge distributions, with complete derivations and solved examples
Topics
Electric Charge: The Basics
What electric charge is, how it was discovered, the two types of charge, positive and negative naming convention, the gold-leaf electroscope, electron transfer during charging, and the difference between conductors, insulators, and semiconductors
Basic Properties of Electric Charge
The three fundamental properties of electric charge: additivity (charges add as scalars), conservation (charge can never be created or destroyed), and quantisation (charge always comes in whole-number multiples of e), with solved numerical examples
Coulomb's Law
The quantitative law governing the force between point charges: its experimental discovery by Coulomb, the inverse-square relationship, the constant k and permittivity of free space, the full vector formulation, and comparison of electric and gravitational forces with worked examples
Forces between Multiple Charges
The principle of superposition for electrostatic forces: how to find the net force on any charge in a multi-charge system by vector-adding individual Coulomb forces, with the general summation formula and fully worked examples on symmetric charge arrangements
Electric Field
The concept of the electric field as a property of space around a charge, its mathematical definition, the relationship between force and field, source and test charges, directional behaviour, and the spherical symmetry of the field due to a point charge
Electric Field Due to a System of Charges and Its Physical Significance
How to find the net electric field from multiple charges using the superposition principle, why the electric field is a real physical entity and not just a mathematical shortcut, and worked examples involving charged particles in uniform and non-uniform fields
Electric Field Lines
How electric field lines give a visual picture of the field around charges, what their density and direction tell us about field strength, the concept of solid angle, and the key properties that field lines must always obey
Electric Flux
How to measure the amount of electric field passing through a surface using the dot product of the field and area vectors, the role of surface orientation, and the convention for closed surfaces
Electric Dipole
What happens when two equal and opposite charges sit close together: the electric dipole, its moment, field derivations on the axis and equatorial plane, the point dipole limit, and polar vs non-polar molecules
Dipole in a Uniform External Field
How an electric dipole behaves when placed in an external field: zero net force but a turning torque in a uniform field, the cross-product formula for torque, alignment tendency, and the contrasting situation in a non-uniform field where a net force appears
Continuous Charge Distribution
How to describe charge spread over lines, surfaces, and volumes using charge densities, the analogy with mass distributions in mechanics, and computing the electric field due to a continuous distribution via Coulomb's law and superposition
Gauss's Law
How the total electric flux through any closed surface depends only on the enclosed charge, with a complete derivation from Coulomb's law, the six key properties of the law, and fully worked examples on cubes and cylinders
Applying Gauss's Law: Electric Field of an Infinite Line Charge
How to use Gauss's law with symmetry arguments and a cylindrical Gaussian surface to derive the electric field around an infinitely long uniformly charged wire, including the full vector result and practical limitations
Applying Gauss's Law: Infinite Plane Sheet and Spherical Shell
Using Gauss's law with planar and spherical symmetry to derive the electric field of a uniformly charged infinite plane sheet and a uniformly charged thin spherical shell, including the shell theorem, the zero-field interior result, and a fully worked early atom model problem