--- 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: 2026-09-12 --- > **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 Ring a charging capacitor with a loop and Ampere's law breaks: no conduction current crosses the gap, yet the loop rule demands one. The fix is the changing electric field between the plates, which acts exactly like a current. This displacement current is mu0 eps0 times the rate of change of electric flux. Add it to the loop rule and the contradiction heals, completing the symmetry between electricity and magnetism. The full set is four statements. Gauss for E: charges source electric fields. Gauss for magnetism: there is no magnetic charge. Faraday: changing magnetic flux rings the region with electric field. Ampere-Maxwell: currents plus changing electric flux ring it with magnetic field. The two change equations feed each other, changing E birthing B birthing E, and the pair propagates as a wave at 1 over sqrt(mu0 eps0). That speed equals the measured speed of light, and Hertz later confirmed the waves with spark-gap antennas. The set is almost symmetric, except one side lacks a source. Electric charges exist alone, but magnetic poles always come in north-south pairs, so the magnetic Gauss law reports zero source. A magnetic monopole would complete the mirror, but none has ever been found. State the four laws in words first; the missing monopole is the one lopsided detail to keep. **Tip.** Answer which-equation questions with this map. Sources of E mean Gauss for E. No monopole means Gauss for magnetism. Changing B means Faraday. Currents or changing E mean Ampere-Maxwell. And remember the hardware moral: an accelerated charge sheds linked E and B ripples that feed each other outward, which is how every transmitter broadcasts and every receiver listens. **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-) - [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)