Field bench

Drag the white handles to reshape the circuit. Double-click the canvas to add a bend.

Point at the field

|E|— B_z— |S|— V—

Field strength

——

What to draw

Rendering

Strength as background colour Direction arrows Field lines Surface charge (+ / −)

Each mark is one equal quantum of charge, so the marks crowd where the surface charge piles up. The loop is neutral, so there are always as many + as −.

Circuit

Battery

LED resistance

Wire resistance

Wire radius

Fatten the wire to see the field in its interior.

Shape

Alt-click or long-press a handle to delete it. Handles in use: —

Numbers

Current—

Power into LED—

Loop length—

E inside plain wire—

E inside LED—

E inside battery—

Peak surface charge—

Push wire resistance off zero and the field inside the plain wire stops being zero. That is Ohm's law, E = ρJ, sitting inside the metal — and the energy flow tips inward along the whole run instead of gliding past it.

How this is computed

The wire is a filament carrying an unknown surface charge. Ohm's law fixes the potential everywhere 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 Biot–Savart. Nothing here is drawn by hand; the field shapes are the solution.

The LED is modelled as a plain resistor, the wire as a thin filament, and everything is shown in the plane of the circuit, where B points purely in and out of the screen.