Equipotential & Electric Field Mapping

Map the invisible

Start with an optional exploration in Explore a question, or build your own arrangement. Predict what will happen before selecting Reveal & explain.

  1. Drag a positive or negative charge from the tray onto the paper, or press its Add button. Move charges to change the field.
  2. Drag the red probe tip across the grid. The voltmeter reads electric potential relative to infinity. Click the grid to move the probe there.
  3. Turn on equipotentials to reveal equal-voltage contours. The dashed probe contour follows the probe’s present voltage; move along it and compare voltage readings. The gold arrow points toward decreasing potential and is perpendicular to the contour. Electric field arrows point in the direction a positive test charge would accelerate.
  4. Compare a single charge, a dipole and like charges. Select a charge to change its strength or remove it.

Tap anywhere on the grid to place the probe. You can add charges with the tray buttons instead of dragging.

Keyboard: Tab to a charge or the probe, then use arrow keys to move it. Hold Shift for larger steps. Delete removes a selected charge.

This is an ideal point-charge sandbox, styled after a conductive-paper lab. It uses V = Σkq/r and E = Σkq r̂/r² in a plane through three-dimensional space. It does not solve a conductive sheet or fixed-voltage electrodes. Values within 1.2 cm of a charge are hidden; the point-charge model is singular there. Nothing is recorded.

Electric field mapping

POINT-CHARGE SANDBOX
CONDUCTIVE-PAPER STYLE GRID 60 × 40 cm

Gold arrow: field direction at the probe, toward lower voltage. Dashed line: probe’s voltage.

Positive potential Negative potential5 cm grid
ZORNSCIENCEDIGITAL VOLTMETER
0.00V DC
V⎓COMV Ω
Move the red probe

x: 30.0 cm · y: 20.0 cm

Reference: V = 0 at infinity

∞   REFERENCE

Electric field: 0 V/m

Drag a charge or the red probe to explore.

About the model

Equipotentials are computed from the summed Coulomb potentials; field arrows show the negative gradient of potential. Red indicates positive potential, blue negative, and white zero. The gold probe arrow shows direction only. Grid arrows use a compressed length scale so weak fields remain visible; use the numerical V/m readout to compare strength. The dashed contour is recalculated at the current probe voltage, not saved. Zero field means there is no preferred direction at that point. The probe does not disturb the charges. The voltmeter has an ideal reference at infinity. Physical thumbtacks on conductive paper instead set electrode voltages and produce a two-dimensional conduction problem.