Van de Graaff Generator

A stylized electrostatic generator integrates belt-delivered charge onto a dome modeled as a capacitor with C proportional to radius (isolated-sphere cartoon). Voltage V = Q/C rises until a user threshold mimics air breakdown; a brief spark partially discharges the dome with a cooldown to avoid rapid re-triggering.

Who it's for: High-school and intro college electrostatics; complements the Coulomb field visualizer and plasma-ball toy.

Key terms

  • electrostatic induction
  • breakdown field
  • capacitance
  • Van de Graaff
  • spark

Live graphs

How it works

A rubber belt driven by rollers carries charge toward a metal dome. Charge accumulates on the dome (modeled as a capacitor whose value grows with radius) until the electric field is large enough for **air breakdown** — then a stylized spark jumps to a grounded electrode and the dome partially discharges.

Key equations

dQ/dt = I_belt − leakage ,   V = Q/C
C ∝ R (isolated-sphere cartoon) · spark when V ≥ V_break

Frequently asked questions

Are the voltages in kilovolts?
No: the plot uses a relative model with an adjustable breakdown threshold. Real Van de Graaff machines can reach megavolts; always follow institutional safety rules around high voltage.
Why does a larger dome radius lower the voltage for the same charge?
With the simple C ∝ R scaling used here, a larger capacitance means less voltage for the same stored charge. That matches the qualitative idea that larger conductors “hold” charge at lower surface fields for the same charge.