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Maxwell's Equations Visualized

Four equations describing all classical electromagnetism.

A free, animated maxwell's equations visualized you can read here or embed on any website, from Scrollchart.

Maxwell's Equations Visualized

Maxwell's Equations VisualizedFour equations that unify electricity, magnetism, and lightGauss's Law (E)∮ E·dA = Q_enc / ε₀Electric flux through any closed surfaceequals enclosed charge divided by ε₀.No charge: zero net fluxGauss's Law (B)∮ B·dA = 0Magnetic flux through any closed surfaceis always zero: no magnetic monopolesB lines always close on themselvesFaraday's Law∮ E·dl = -dΦ_B/dtA changing magnetic flux induces acirculating electric field (EMF). MinusGenerator, transformer principleAmpere-Maxwell Law∮ B·dl = μ₀(I + ε₀ dΦ_E/dt)Magnetic circulation = conduction currentplus displacement current. DisplacementPredicts c = 1/√(ε₀μ₀)+QNSI_indIBMaxwell (1865): four equations predict light speed c = 1/sqrt(ε₀μ₀), unifying optics with electromagnetism

Four panels: Gauss for E, Gauss for B (no monopoles), Faraday, Ampere-Maxwell. Each with integral form and visual interpretation.

Good for

  • University electromagnetism courses covering all four Maxwell equations
  • Physics explainer articles on the unification of electricity and magnetism
  • Engineering courses on electromagnetic wave propagation and antenna design

Source & accuracy

This maxwell's equations visualized is an editorial illustration built to represent the concept accurately. Where it shows figures, they are typical or representative values chosen to make the relationship clear, not a single underlying dataset. The diagram and its explainer are reviewed and maintained centrally, and updated over time as understanding improves.

Four laws unifying electricity, magnetism, and light

Maxwell's four equations form the foundation of electromagnetism. Gauss's law relates electric field to charge. Gauss's law for magnetism states that magnetic field lines have no beginning or end (no magnetic monopoles exist). Faraday's law connects changing magnetic flux to induced electric field. Ampere-Maxwell law connects electric current and changing electric flux to magnetic field. Together, these equations reveal that electricity and magnetism are not separate phenomena but aspects of a single electromagnetic field. A charge creates electric field. Moving charge creates magnetic field. Changing electric field creates magnetic field. Changing magnetic field creates electric field. These interconnections enable electromagnetic waves to propagate through empty space, with fields continuously regenerating each other.

Implications for light and modern technology

Maxwell's equations predict that electromagnetic waves travel at light speed, leading to the realization that light itself is an electromagnetic phenomenon. This unification explained long-mysterious properties of light and revealed its place on the broader electromagnetic spectrum. The equations enabled the design of antennas, radio transmitters, and all wireless communication systems. They guided the development of technologies from radar to microwave ovens. Quantum mechanics later confirmed that light consists of photons, but Maxwell's classical wave equations remain accurate for most practical applications. The equations' elegance and predictive power revolutionized physics, demonstrating how seemingly disparate forces unite under a deeper principle. Their symmetries have inspired modern particle physics theories seeking similar unifications of other fundamental forces.

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Reference

What this is
A free, embeddable, animated maxwell's equations visualized for any website.
Who uses it
Physics educators.
How to embed
Copy one line of HTML. No signup. No watermark. Works in WordPress, Webflow, Ghost, Substack, plain HTML.
File size
iframe embed, ~80 KB gzipped (loads on demand, does not block your page paint).
License
Free forever. Editorial explainer text included; updated centrally over time.

Embed format options

Copy the universal HTML snippet, the WordPress shortcode, or an iframe fallback - see the WordPress plugin page for details. Any format keeps the same Core Web Vitals profile and the same explainer text.

Embed snippet
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Frequently asked questions

Where can I get a free animated "Maxwell's Equations Visualized" for my website?
Scrollchart provides "Maxwell's Equations Visualized" as a free, embeddable animated diagram you can add to any website with one line of HTML. No signup is required and there is no watermark. The diagram and its explainer text are served from scrollchart.com, so the embed stays current without any maintenance on your end.
How do I embed a maxwell's equations visualized in WordPress or a static site?
Paste the HTML snippet from the Scrollchart diagram page into your WordPress post (in HTML/code view), your Webflow embed block, or directly into a static HTML file. No plugin is needed. The diagram loads from scrollchart.com and paints in as the reader scrolls.