A closed surface with the charge inside
At its defaults it draws a closed surface with the charge inside. Every field line from the enclosed charge crosses the surface exactly once on its way out, so the net flux counts the charge.
gaussian-surface is one function in lib/figures/fields.js —
charge, current, flux and the lines drawn between them. Everything below came out
of it during this build, at parameters taken from the essays rather than invented for this
page. A figure here is the figure a reader meets in an essay, and if the generator changes,
this page changes with it.
At its defaults
Drawn even though every essay passes options, because a default nothing exercises is a trap for the next essay to call this with none — which has happened here twice.
Every field line from the enclosed charge crosses the surface exactly once on its way out, so the net flux counts the charge.
A closed surface with the charge inside
The options are the ones Counting what comes out, and never looking inside passes. A branch drawn at its own defaults instead would be a picture no essay asked for and no assertion has been run against.
Every field line from the enclosed charge crosses the surface exactly once on its way out, so the net flux counts the charge.
A closed surface with the charge outside
The options are the ones Counting what comes out, and never looking inside passes. A branch drawn at its own defaults instead would be a picture no essay asked for and no assertion has been run against.
Each line from the outside charge that enters the surface also leaves it, so the crossings cancel and the net flux is zero.
A closed surface with the charge inside
The options are the ones Counting what comes out, and never looking inside passes. A branch drawn at its own defaults instead would be a picture no essay asked for and no assertion has been run against.
Every field line from the enclosed charge crosses the surface exactly once on its way out, so the net flux counts the charge.
A closed surface with the charge inside
The options are the ones Counting what comes out, and never looking inside passes. A branch drawn at its own defaults instead would be a picture no essay asked for and no assertion has been run against.
Every field line from the enclosed charge crosses the surface exactly once on its way out, so the net flux counts the charge.
A closed surface with the charge outside
The options are the ones Counting what comes out, and never looking inside passes. A branch drawn at its own defaults instead would be a picture no essay asked for and no assertion has been run against.
Each line from the outside charge that enters the surface also leaves it, so the crossings cancel and the net flux is zero.
What checks it
physicscheck draws gaussian-surface and asserts nothing about
its physics — it is exercised by the branch table rather than interrogated.
Across the library: 100 interrogated, 2 exercised only, 1 untouched, of 103. Read out of the gate's source by the gate's own two patterns — and the gate's last claim fails the build if that read disagrees with what it was handed while running.
Where it is called
Changing this generator changes every figure on this list. That is what makes the list worth publishing rather than keeping in a check script.
Counting what comes out, and never looking inside
Draw any closed surface. The field crossing it depends only on the charge enclosed — not on where that charge sits, not on its shape, not on anything outside.
ElectromagnetismHow much charge a shape will hold, before anything is charged
Capacitance is decided by geometry alone. Two pieces of metal have a number attached to them, fixed by their shape and their separation, and it is settled before any charge arrives.
ElectromagnetismThe shape decides the falloff, and the force law never changes
A point charge gives an inverse square, a line gives an inverse, a plane gives a constant. All three come from the same law, and the exponent belongs to the geometry of the source rather than to the physics.