Interactive Laplace Solver: Draw Your Own Conductors

In a charge-free region the electrostatic potential obeys Laplace's equation, del^2 V = 0, which has the smoothing property that V at any point is the average of its neighbours and can have no interior maximum or minimum. The primary canvas is the potential field itself with electric-field streamlines; you drag to paint conductors, pick presets (parallel plates, coaxial cable, dipole, charged sphere), set the voltage, and switch between the potential, the field magnitude |E|, and equipotential views. Watching the solution relax shows the potential settling into the unique configuration fixed by the conductor boundaries, with E always perpendicular to them.