# Electricity & Magnetism

Electricity and magnetism begin with a single quantity — **charge** —
and the field it fills space with. Every force, potential, and current in the
subject is bookkeeping on that field and how it changes.


_Figure 001 — A dipole's field: lines stream out of the positive charge and terminate on
the negative one, never crossing.
_

A charge sources an **electric field**, and a field exerts a force on
any charge placed in it. Draw the field as lines — dense where it is strong,
always leaving _+_ and landing on _−_ — and most of electrostatics
becomes a picture you can read.


Two ideas make fields tractable. **Potential** collapses a vector
field to a single scalar you can add up; **flux**, through Gauss's law,
turns a surface integral into the charge enclosed. Symmetry then does the rest.


_Figure 002 — A parallel-plate capacitor: opposite charges on two plates make a uniform
field in the gap.
_

Store charge on conductors and you get **capacitance**; let it flow and
you get **current**, **resistance**, and the circuits that move
energy from one place to another.


Moving charge is the bridge to magnetism. A current sets up a
**magnetic field** that circulates around it, and Ampère's law ties the
field to the current the same way Gauss's law ties _E_ to charge.


_Figure 003 — A current loop threads a field through its centre — a magnetic dipole, the
atom of magnetism.
_

The two fields are not independent. A **changing magnetic flux** drives an
electric field around a loop — Faraday's law of induction — which is how every
generator, transformer, and inductor works.


_Figure 004 — Induction: a magnet moving through a coil changes the flux and drives a
current, opposing the change.
_

Maxwell added the missing symmetry — a changing electric field is itself a
source of magnetic field — and the four equations closed on themselves. A
field could now sustain a field, with no charges in sight.


_Figure 005 — An electromagnetic wave: <em>E</em> and <em>B</em> oscillate perpendicular and in
phase, travelling at <em>c</em>.
_

That self-sustaining ripple is **light**. Electromagnetic waves carry
energy and momentum, come in every wavelength, and — through reflection and
refraction — hand the subject over to optics.


---

## Contents

### 1. Electric Fields

1. [Charge and Conductors](/electricity-and-magnetism/electric-fields/charge-and-conductors)
2. [Coulomb's Law](/electricity-and-magnetism/electric-fields/coulombs-law)
3. [Electric Field and Force](/electricity-and-magnetism/electric-fields/electric-field-and-force)
4. [Electric Field Maps](/electricity-and-magnetism/electric-fields/electric-field-maps)
5. [Electric Dipoles](/electricity-and-magnetism/electric-fields/electric-dipoles)

### 2. Continuous Charge Distributions

1. [Continuous Charge Fields](/electricity-and-magnetism/continuous-charge-distributions/continuous-charge-fields)
2. [Gauss's Law and Conductors](/electricity-and-magnetism/continuous-charge-distributions/gauss-law-and-conductors)

### 3. Electric Potential

1. [Point-Charge Potential](/electricity-and-magnetism/electric-potential/point-charge-potential)
2. [Potential Gradients and Equipotentials](/electricity-and-magnetism/electric-potential/potential-gradients-and-equipotentials)
3. [Electrostatic Energy and Pressure](/electricity-and-magnetism/electric-potential/electrostatic-energy-and-pressure)
4. [Laplace Boundary Problems](/electricity-and-magnetism/electric-potential/laplace-boundary-problems)
5. [Continuous Charge Potentials](/electricity-and-magnetism/electric-potential/continuous-charge-potentials)

### 4. Capacitance

1. [Capacitance Fundamentals](/electricity-and-magnetism/capacitance/capacitance-fundamentals)
2. [Capacitor Networks](/electricity-and-magnetism/capacitance/capacitor-networks)
3. [Capacitor Energy and Force](/electricity-and-magnetism/capacitance/capacitor-energy-and-force)
4. [Dielectric Polarization and Breakdown](/electricity-and-magnetism/capacitance/dielectric-polarization-and-breakdown)

### 5. Direct-Current Circuits

1. [Current and Resistance](/electricity-and-magnetism/direct-current-circuits/current-and-resistance)
2. [Kirchhoff Network Analysis](/electricity-and-magnetism/direct-current-circuits/kirchhoff-network-analysis)
3. [RC Transients](/electricity-and-magnetism/direct-current-circuits/rc-transients)

### 6. Magnetic Field

1. [Magnetic Trajectories](/electricity-and-magnetism/magnetic-field/magnetic-trajectories)
2. [Hall Effect](/electricity-and-magnetism/magnetic-field/hall-effect)
3. [Magnetic Force on Conductors](/electricity-and-magnetism/magnetic-field/magnetic-force-on-conductors)
4. [Magnetic Dipoles](/electricity-and-magnetism/magnetic-field/magnetic-dipoles)
5. [Mass Spectrometry](/electricity-and-magnetism/magnetic-field/mass-spectrometry)

### 7. Magnetic Sources

1. [Moving-Charge Fields](/electricity-and-magnetism/magnetic-sources/moving-charge-fields)
2. [Biot–Savart Law](/electricity-and-magnetism/magnetic-sources/biot-savart-law)
3. [Circular Current Loops](/electricity-and-magnetism/magnetic-sources/circular-current-loops)
4. [Ampère’s Law](/electricity-and-magnetism/magnetic-sources/amperes-law)
5. [Gauss’s Law for Magnetism](/electricity-and-magnetism/magnetic-sources/gauss-law-for-magnetism)
6. [Magnetic Materials](/electricity-and-magnetism/magnetic-sources/magnetic-materials)

### 8. Electromagnetic Induction

1. [Magnetic Flux](/electricity-and-magnetism/electromagnetic-induction/magnetic-flux)
2. [Faraday's Law](/electricity-and-magnetism/electromagnetic-induction/faradays-law)
3. [Lenz's Law](/electricity-and-magnetism/electromagnetic-induction/lenzs-law)
4. [Motional EMF](/electricity-and-magnetism/electromagnetic-induction/motional-emf)
5. [Eddy Currents](/electricity-and-magnetism/electromagnetic-induction/eddy-currents)
6. [Self-Inductance](/electricity-and-magnetism/electromagnetic-induction/self-inductance)
7. [Magnetic Energy](/electricity-and-magnetism/electromagnetic-induction/magnetic-energy)
8. [RL Circuits](/electricity-and-magnetism/electromagnetic-induction/rl-circuits)

### 9. Alternating Current

1. [AC Fundamentals](/electricity-and-magnetism/alternating-current/ac-fundamentals)
2. [Reactance](/electricity-and-magnetism/alternating-current/reactance)
3. [RLC Resonance](/electricity-and-magnetism/alternating-current/rlc-resonance)
4. [AC Power](/electricity-and-magnetism/alternating-current/ac-power)
5. [Transformers](/electricity-and-magnetism/alternating-current/transformers)

### 10. Maxwell’s Equations and Electromagnetic Waves

1. [Displacement Current](/electricity-and-magnetism/maxwell-electromagnetic-waves/displacement-current)
2. [Electromagnetic Waves](/electricity-and-magnetism/maxwell-electromagnetic-waves/electromagnetic-waves)
3. [Electromagnetic Momentum](/electricity-and-magnetism/maxwell-electromagnetic-waves/electromagnetic-momentum)
4. [Dipole Radiation](/electricity-and-magnetism/maxwell-electromagnetic-waves/dipole-radiation)
5. [Polarization](/electricity-and-magnetism/maxwell-electromagnetic-waves/polarization)

### 11. Geometrical Optics

1. [Reflection and Refraction](/electricity-and-magnetism/optics/reflection-and-refraction)
2. [Thin Lenses](/electricity-and-magnetism/optics/thin-lenses)
3. [Spherical Mirrors](/electricity-and-magnetism/optics/spherical-mirrors)