The same field, sampled as arrows
At its defaults it draws the same field, sampled as arrows. The field at a grid of points, each arrow pointing the way a positive test charge would be pushed and scaled by the strength there.
vector-field 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.
The field at a grid of points, each arrow pointing the way a positive test charge would be pushed and scaled by the strength there.
The field of a dipole
The options are the ones Field lines are a choice, not a discovery passes. A branch drawn at its own defaults instead would be a picture no essay asked for and no assertion has been run against.
Field lines traced from a positive charge toward a negative one. Every line does eventually close on the negative charge, but the outer ones loop far outside any frame, so this picture is a crop rather than the whole field.
The same field, sampled as arrows
The options are the ones Field lines are a choice, not a discovery passes. A branch drawn at its own defaults instead would be a picture no essay asked for and no assertion has been run against.
The field at a grid of points, each arrow pointing the way a positive test charge would be pushed and scaled by the strength there.
The field of a single charge
The options are the ones Field lines are a choice, not a discovery passes. A branch drawn at its own defaults instead would be a picture no essay asked for and no assertion has been run against.
Field lines radiating from one positive charge, straight and evenly spread.
The field of two like charges
The options are the ones Field lines are a choice, not a discovery passes. A branch drawn at its own defaults instead would be a picture no essay asked for and no assertion has been run against.
Field lines from two positive charges. None connects them; between them is a point where the field vanishes entirely.
Every stationary point has a way out
The options are the ones Nothing can be held still by a static field passes. A branch drawn at its own defaults instead would be a picture no essay asked for and no assertion has been run against.
The potential along four lines through the most symmetric point of a symmetric arrangement of 4 equal charges at the corners of a square — the one place a trap might be expected. In the plane of the square the potential rises in every direction; out of the plane it falls. The point is stationary and it is a saddle, which is what Laplace's equation forces: the three second derivatives must sum to zero — computed here as 1.4e-5 against the individual values of order 2e+0 — so if two of them are positive the third must be negative. A particle released here rolls away along the direction that falls. No amount of ingenuity in placing the charges changes this, because the constraint is on the equation rather than on the arrangement, and it is why every real trap for a charged particle either uses time-varying fields, or a magnetic field with a velocity, or a material with a negative response.
What checks it
physicscheck does not draw vector-field at all.
Its figures are checked for overflow, contrast, legibility and markup by the shared gates and
for nothing about the physics — a debt recorded in _plan/PHASE_PLAN.md since the
scale phase, published here so it is visible from the site rather than only from
the gate.
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.
Field lines are a choice, not a discovery
Nothing in space is arranged in lines. The lines are a drawing convention — and an unusually good one, because three separate facts about the field survive the translation.
ElectromagnetismNothing can be held still by a static field
However many charges are arranged, however cleverly, a charge placed among them has somewhere to fall. The reason is one line of arithmetic — the potential in empty space satisfies Laplace's equation, and a solution of that equation has no interior maximum or minimum — and the consequence is that every real trap for a charged particle works by breaking one of the assumptions rather than by being cleverer.
ElectromagnetismOne number for every point, and nothing at all is lost
The electric field is three numbers at every point of space. Replacing it with one number loses nothing — and the reason it loses nothing is the same reason a hill can be drawn as a contour map.
ElectromagnetismThe attraction that needs no charge
Gauss's law says nothing comes out of a neutral molecule, and yet water's field one nanometre away reaches 1.1 × 10⁸ V/m. What survives when the monopole vanishes is a separation, and every step down the tower of falloffs below it is paid for with one more order of cancellation.
ElectromagnetismThe field before the lines were drawn on it
A field is a vector attached to every point of space. Drawing it as arrows on a grid is honest and ugly; drawing it as lines is beautiful and throws information away.
ElectromagnetismThe potential is where the wanderers stop
Start a random walker at a point between charged conductors and let it wander until it touches one of them. The average potential of the surfaces the walkers touch is the potential at the starting point — exactly, with no equation solved — and the charge a conductor keeps at each place on its surface is the chance that a walker arriving from far away touches it there first.