Field bench 3D

Drag the background to orbit, a white handle to reshape the loop. Scroll to zoom.

Point at the slice

|E|— |B|— |S|— V—

Field strength

——

What to draw

Viewpoint

Rotate (azimuth)—

Tilt (elevation)—

Zoom (distance)—

Lens (field of view)—

Turn it slowly

Drag the background to orbit and scroll to zoom; the sliders do the same thing. A narrow lens flattens the perspective, a wide one exaggerates depth.

Slice plane

Offset—

A flat cut through the field, for the colour map and for the readout: hovering reports the field where the cursor's line of sight crosses this plane. With z = 0 and a flat loop it is the planar field bench, seen from wherever you happen to be standing.

Rendering

Arrows along the field lines The field lines themselves Surface charge (+ / −) Strength as colour on the slice Outline the slice

Arrow size—

Field lines are seeded on a lattice filling the space around the circuit, and the arrows ride on them: a line's tangent is the field direction, so an arrow on a line already points the right way. The two switch independently — arrows alone give a flow without the curves. Arrows in weak field fade rather than being cut off, so what thins out is the field thinning out.

Circuit

Battery—

LED resistance—

Wire resistance—

Wire radius—

Fatten the wire to see the field in its interior.

Shape

Dragging a handle moves it in the plane of the screen, so orbit first, then drag: the direction you push it depends on where you are looking from. Handles in use: 8

Numbers

Current—

Power into LED—

Loop length—

E inside plain wire—

E inside LED—

Peak surface charge—

How this is computed

The wire is a closed filament in space carrying an unknown line charge density. Ohm's law fixes the potential along it — flat along ideal wire, sloping across the LED, stepping up across the battery — so the charge is whatever reproduces that potential. The app solves that boundary-value problem, then takes E from Coulomb and B from the exact field of each finite straight filament.

The Coulomb kernel was always three-dimensional, so the charge solve is the same one the planar bench does. What is new is that B is a full vector rather than one component, which is why the loop no longer has to lie in a plane.