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Maxwell Equations, Displacement Current, and Potentials

First-principles derivation of Maxwell's equations, current continuity, and electromagnetic potentials.

Consider a small wave on the free surface of an incompressible, inviscid liquid of density $\rho$. Take the undisturbed surface as $z=0$, with...

A molecule well inside a liquid is attracted in all directions. A molecule near the surface has fewer neighbours on the vapour side, so work m...

For an incompressible liquid, the volume rate is the same at every cross-section. A gas expands as its pressure falls, so its local volume rat...

A viscous fluid resists relative motion between neighbouring layers. For a Newtonian fluid moving in the $z$ direction with speed $v_z(x)$, th...

An external force changes the relative positions of the particles of a solid. When the force is removed, interatomic forces tend to restore th...

How to update About, Ref, Notes Archive, header contact icons, share icons, and site identity from _data and _config.yml.

A practical guide to fenced code blocks, language names, copy buttons, inline code, and mobile-safe code examples.

A practical guide to editing the segmented Sass files inside the _sass directory without touching one huge CSS file.

The basic local checks to run after editing posts, styles, assets, or templates.