Electrostatics

Electric Potential

WebGPU Context Active

Parameters

Display
Equipotential Lines
E-Field Vectors
Q1
Probe Readout

Hover over the simulation to probe potential.

V(x) Profile — Horizontal Center
V (Volts)
V(y) Profile — Vertical Center
V (Volts)
  • Red regions: Positive potential.
  • Blue regions: Negative potential.
  • Orange lines: Positive equipotentials.
  • Cyan lines: Negative equipotentials.

Governing Dynamics

The electric potential at a point is the work per unit charge to bring a test charge from infinity:

V=ke∑iqiriV = k_e \sum_{i} \frac{q_i}{r_i}

The electric field is the negative gradient of the potential:

E⃗=−∇V=∑ikeqiri2r^i\vec{E} = -\nabla V = \sum_{i} k_e \frac{q_i}{r_i^2} \hat{r}_i

Equipotential lines are always perpendicular to electric field lines. No work is done when a charge moves along an equipotential.