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.

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.

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