Electric Potential 3D Surface Lab
See the electric potential V(x, y) come to life as a 3D height map. Add or remove point charges, adjust their positions, and watch the surface morph in real time. Toggle equipotential contours and field arrows to connect the geometry of V to the force-bearing E-field.
Drag to orbit. Scroll to zoom. The 3D surface shows the electric potential V(x, y) over the plane. Red peaks correspond to positive charges, blue valleys to negative charges. Equipotential contours on the floor show level sets of V.
Controls
Charges
Display
Presets
Reference Guide
Electric Potential
The electric potential at a point is the energy per unit charge needed to bring a test charge there from infinity.
Units are volts (J/C). Positive charges produce peaks; negative charges produce wells.
Field and Gradient
The electric field is minus the gradient of the potential.
E always points downhill on the V surface, perpendicular to the equipotential contours.
Equipotentials
A surface where V is constant. No work is done moving a charge along an equipotential.
For a single point charge equipotentials are concentric spheres. Two charges produce more complex shapes including the famous figure-8 saddles.
The Dipole
Two equal and opposite charges separated by distance d. The far-field potential along the dipole axis falls as 1/r²:
Dipoles are the building blocks of polar molecules, antennas, and dielectric polarization.
