--- title: "Displacement Current and Maxwell's Equations" description: "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 " canonical: https://lightmysky.com/learn/science/displacement-current-and-maxwells-equations-mt_YR8m8TNfyy source: https://lightmysky.com/learn/science/displacement-current-and-maxwells-equations-mt_YR8m8TNfyy.md retrieved: 2026-11-12 --- > **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`. # Displacement Current and Maxwell's Equations 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. Subject: Science · Area: Electricity & Magnetism · Ages 20 to 22 Page: https://lightmysky.com/learn/science/displacement-current-and-maxwells-equations-mt_YR8m8TNfyy ## Ready when they can - Shows where Ampere's law breaks down between capacitor plates and what the extra term fixes - States all four equations in words and names the physical content of each - Explains why the set is symmetric except for the absence of magnetic charge ## Lesson: Fixing Ampere's law: displacement current and Maxwell's set Draw a loop around a wire that feeds a charging capacitor. Ampere's law takes the current through any surface bounded by the loop. A flat surface cut by the wire gives I, but a bulging surface that passes between the plates meets no wire and gives zero. Maxwell fixed the clash: the changing electric flux between the plates acts like a current. Eps0 times its rate of change is the displacement current, so the loop rule gains mu0 eps0 times that rate. The full set has four laws. Gauss for E: electric charges are the sources of electric field. Gauss for magnetism: the magnetic flux through any closed surface is zero, so there is no magnetic charge. Faraday: changing magnetic flux makes a curling electric field. Ampere-Maxwell: currents plus changing electric flux make a curling magnetic field. The set is almost symmetric. Electric charges exist alone, but magnetic field lines have no beginning or end. Cut a bar magnet and each piece still has a north and a south pole. A lone pole, called a magnetic monopole, would give the magnetic Gauss law a source, but none has been found. That missing source is the one gap in the mirror between the electric and magnetic laws. **Tip.** Match a question to its law. Sources of E point to Gauss for E. No magnetic charge points to Gauss for magnetism. Changing B points to Faraday. Currents or changing E point to Ampere-Maxwell. **Recap.** Changing electric flux repairs Ampere's law as displacement current, the four laws close into light-speed waves, and only the missing monopole spoils the symmetry. ## Practice 8 questions on this page, each with its working shown. ## Needs first - [Induced Electric Fields and Motional EMF](https://lightmysky.com/learn/science/induced-electric-fields-and-motional-emf-mt_LpmHnz46tu) - [Stokes' Theorem and the Divergence Theorem](https://lightmysky.com/learn/mathematics/stokes-theorem-and-the-divergence-theorem-mt_sRojZcrw-q) - [Ampere's Law: Wires, Solenoids and Toroids](https://lightmysky.com/learn/science/amperes-law-wires-solenoids-and-toroids-mt_uTzRcSiUQ-) ## Optional connections - [Resonance and Power in AC Circuits](https://lightmysky.com/learn/science/resonance-and-power-in-ac-circuits-mt_wviaR0dJud) ## Opens up - [Plane Electromagnetic Waves from Maxwell's Equations](https://lightmysky.com/learn/science/plane-electromagnetic-waves-from-maxwells-equations-mt_27tbaYcxCM) - [Covariant Electrodynamics and the Field Tensor](https://lightmysky.com/learn/science/covariant-electrodynamics-and-the-field-tensor-mt_RoxM9z6DfK)