--- title: "Electricity & Magnetism" description: "23 topics in Science, in the order they build on each other." canonical: https://lightmysky.com/learn/science/areas/electricity-and-magnetism source: https://lightmysky.com/learn/science/areas/electricity-and-magnetism.md retrieved: 2026-09-02 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # Electricity & Magnetism 23 topics in Science, in the order they build on each other. Page: https://lightmysky.com/learn/science/areas/electricity-and-magnetism - [The Electric Field of a Continuous Charge Distribution](https://lightmysky.com/learn/science/the-electric-field-of-a-continuous-charge-distribution-mt_IIcVqWapC1): A charged rod or ring is treated as an infinite set of point charges, so the field becomes an integral of Coulomb contributions. Symmetry decides which components cancel before any integration starts. - [Electric Flux and Gauss's Law](https://lightmysky.com/learn/science/electric-flux-and-gausss-law-mt_Z5dZQvik6o): Flux counts how much field passes through a surface, and Gauss's law says the flux out of any closed surface is set only by the charge inside. The shape of the surface is free, which is what makes the law useful. - [Applying Gauss's Law to Symmetric Charge Distributions](https://lightmysky.com/learn/science/applying-gausss-law-to-symmetric-charge-distributions-mt_1LZboKPJ4D): For spherical, cylindrical or planar symmetry, Gauss's law gives the field in a line of algebra where the direct integral would be heavy. The work is all in choosing the surface and arguing the symmetry. - [Conductors, Shielding and Surface Charge](https://lightmysky.com/learn/science/conductors-shielding-and-surface-charge-mt_2zmzTE-dgL): In electrostatic equilibrium the field inside a conductor is zero, all excess charge sits on the surface, and the field just outside is perpendicular to it. A closed conducting shell shields whatever is inside it. - [Calculating Electric Potential from a Charge Distribution](https://lightmysky.com/learn/science/calculating-electric-potential-from-a-charge-distribution-mt_B4WiVkpH4j): Potential is a scalar, so contributions add without any concern for direction, which usually makes it easier to compute than the field. For a continuous body it is again an integral over the charge. - [Recovering the Field from the Potential Gradient](https://lightmysky.com/learn/science/recovering-the-field-from-the-potential-gradient-mt_EqCLB9bqG1): The field is minus the gradient of the potential, so a map of potential contains the field everywhere. Equipotential surfaces are perpendicular to field lines, and the field is strongest where they crowd together. - [Dielectrics and the Polarisation of Matter](https://lightmysky.com/learn/science/dielectrics-and-the-polarisation-of-matter-mt_OYRr_k3IW6): An insulator in a field develops aligned dipoles whose own field opposes the applied one, cutting the field inside by the dielectric constant. That is why filling a capacitor with plastic raises its capacitance. - [Current Density, Drift Velocity and the Microscopic Ohm's Law](https://lightmysky.com/learn/science/current-density-drift-velocity-and-the-microscopic-ohms-law-mt_QU-HkQrkFV): Current is charge crossing an area per second, and inside a metal it comes from a slow drift superposed on fast random motion. Writing current density as conductivity times field turns Ohm's law into a statement about the material. - [Kirchhoff's Rules for Multi-Loop Circuits](https://lightmysky.com/learn/science/kirchhoffs-rules-for-multi-loop-circuits-mt_AS3KiGstGD): The junction rule is charge conservation and the loop rule is energy conservation, and together they give enough equations to solve any network. Sign conventions are the only real difficulty. - [The Biot-Savart Law and the Field of a Current Element](https://lightmysky.com/learn/science/the-biot-savart-law-and-the-field-of-a-current-element-mt_RRsHUaXrFq): Each short piece of current makes a magnetic field that circles it, falling off with the square of the distance, and the total field is the integral of those contributions. It is the magnetic counterpart of the Coulomb integral. - [Ampere's Law: Wires, Solenoids and Toroids](https://lightmysky.com/learn/science/amperes-law-wires-solenoids-and-toroids-mt_uTzRcSiUQ-): The line integral of the magnetic field around a closed loop equals the enclosed current, which gives the field of symmetric arrangements in a line of algebra. A long solenoid comes out uniform inside and near zero outside. - [Induced Electric Fields and Motional EMF](https://lightmysky.com/learn/science/induced-electric-fields-and-motional-emf-mt_LpmHnz46tu): A changing magnetic flux produces a real electric field that pushes charge round a loop, whether the flux changes because the field changes or because the circuit moves. Both readings give the same EMF for a rod sliding on rails. - [Magnetisation: Diamagnetism, Paramagnetism and Ferromagnetism](https://lightmysky.com/learn/science/magnetisation-diamagnetism-paramagnetism-and-ferromagnetism-mt_1apyQ1_1gg): Matter in a magnetic field acquires a magnetisation of its own, weakly opposing the field, weakly aligning with it, or aligning strongly and staying that way. Ferromagnetic order comes from an interaction between neighbouring moments and disappears above the Curie temperature. - [Self-Inductance and Energy Stored in a Magnetic Field](https://lightmysky.com/learn/science/self-inductance-and-energy-stored-in-a-magnetic-field-mt_BLyLSJT-Fr): A coil opposes changes in its own current through the flux it links with itself, and the energy that opposition stores can be written as an energy density spread through the field. Inductance is the magnetic partner of capacitance. - [Oscillations in LC and RLC Circuits](https://lightmysky.com/learn/science/oscillations-in-lc-and-rlc-circuits-mt_QJsqX7xzkZ): Charge sloshing between a capacitor and an inductor obeys the same equation as a mass on a spring, with resistance playing the part of damping. The electrical and mechanical problems share every solution. - [Impedance and Phasors in AC Circuits](https://lightmysky.com/learn/science/impedance-and-phasors-in-ac-circuits-mt_vQVlVWv2ln): Resistors, capacitors and inductors each set a different phase between current and voltage, and rotating phasors add those voltages without trigonometric identities. Impedance packages size and phase in one quantity. - [Resonance and Power in AC Circuits](https://lightmysky.com/learn/science/resonance-and-power-in-ac-circuits-mt_wviaR0dJud): At the frequency where the two reactances cancel, the impedance is smallest and the current peaks, which is how a radio picks one station. Average power depends on the power factor, so a purely reactive load consumes nothing. - [Displacement Current and Maxwell's Equations](https://lightmysky.com/learn/science/displacement-current-and-maxwells-equations-mt_YR8m8TNfyy): Ampere's law fails for a charging capacitor until a term for changing electric flux is added, and with it the four equations close on each other. They say that changing fields of either kind make the other. - [Plane Electromagnetic Waves from Maxwell's Equations](https://lightmysky.com/learn/science/plane-electromagnetic-waves-from-maxwells-equations-mt_27tbaYcxCM): Combining the two induction equations in empty space gives a wave equation whose speed is fixed by two measured electric and magnetic constants. That speed came out equal to the measured speed of light, which is why light is an electromagnetic wave. - [The Poynting Vector and Radiation Pressure](https://lightmysky.com/learn/science/the-poynting-vector-and-radiation-pressure-mt_dwTbNlzBgE): The cross product of the electric and magnetic fields gives the energy flowing through unit area per second, and the same wave carries momentum. Light therefore pushes on what absorbs it, twice as hard if the surface is a mirror. - [Covariant Electrodynamics and the Field Tensor](https://lightmysky.com/learn/science/covariant-electrodynamics-and-the-field-tensor-mt_RoxM9z6DfK): Collecting the fields into one antisymmetric tensor turns Maxwell's four equations into two and makes the split between electric and magnetic a matter of frame. Charge density and current become a single four-vector. - [Gauge Freedom and the Potentials as the Working Variables](https://lightmysky.com/learn/science/gauge-freedom-and-the-potentials-as-the-working-variables-mt_BovDzq3WZm): The potentials are not unique: a whole family of them gives the same fields, and choosing a gauge is choosing which member to work with. Once a gauge is fixed, Maxwell's equations become wave equations with sources. - [Radiation from an Accelerating Charge](https://lightmysky.com/learn/science/radiation-from-an-accelerating-charge-mt_Qr0rMEOYAg): A charge that accelerates radiates power growing with the square of the acceleration, and it radiates sideways rather than along its motion. Antennas, synchrotron light and the reddening of a setting sun all rest on this result.