Extras · Physics teaching tools
Electrostatic field simulator
A virtual conductive-paper sheet for PHY 151 — Relating Electric Fields to Electric Potential. Put a charged disc and a grounded bar on the paper, and the page solves Laplace’s equation over the whole sheet. Then explore the equipotentials, follow the field lines, and check right angles the way you would with the four-point probe and the signal probe in the lab.
Reading the sheet
Six things to try in two minutes
The simulator reproduces the two-piece conductor setup from the lab, so every exploration below carries over to the real paper.
Right angles
Field lines must cross equipotentials at 90°. With E vectors on and contours on, pick a point away from both conductors and check that the arrow meets the contour squarely.
Face the point
Drag the point conductor to the sheet center and slide the bar out to the edge. Equipotentials become circles and field lines become radial — a clean symmetry check.
Probe the falloff
Click the paper and drag to read V and |E|. The field drops sharply inside a couple of centimeters of the disc, then flattens — the same behavior you log with the four-point probe.
Walk a loop
∮E·dl around any closed path is zero, which is what lets a single V exist at all. Drag the probe around a small loop and watch V return to nearly its starting value.
Raise the dielectric
Bump εᵣ from 1 to 10. Nothing moves — V and E are εᵣ-independent at fixed conductor voltages — while C* and U* grow. That is the honest physics, not a bug.
Fly the surface
Open the 3D potential view and drag to rotate. Height is V; the disc rises to V₀, the bar sits at 0, and the saddle between them is where the field lines bend hardest.
Under the hood
How the field is computed
The solver
The sheet is sampled at 8 cells/cm — 241 × 145 cells for the default 30 × 18 cm paper; the Sheet size control scales the whole experiment from half to double size at that same resolution. The code sets V₀ on the disc and 0 V on the bar, then solves Laplace’s equation with a conjugate-gradient iteration preconditioned by a five-level multigrid V-cycle. Paper edges are insulating, so potential cannot leak across them. A solve reaches the field to about a tenth of a percent of V₀ in roughly fifty steps — a fraction of a second in the browser.
The reading
E is the negative gradient of V, taken with clamped (one-sided) differences at the paper edges and forced to zero inside the conductors. Field lines are integrated with a fourth-order Runge–Kutta step along E, seeded just outside the disc; equipotentials are extracted with a marching-squares contour. The pointer, the readouts, and the colormap all share the same field arrays.