Van de Graaff Generator
Charge it up, see sparks. Builds on Coulomb's Law.
A Van de Graaff generator uses a moving belt to carry charge up to a large hollow metal dome. After running for a while, the dome accumulates a significant amount of excess charge.
Where does all the excess charge end up on the dome?
All the charge migrates to the outer surface! This isn’t a quirk of the dome’s shape — it’s a fundamental law. Inside any conductor, the electric field is zero. If charge were anywhere inside, it would create a field and move. The only stable configuration is all excess charge on the outside. This is why the Van de Graaff works: charge deposited inside the dome immediately rushes to the outer surface, leaving the interior ready to accept more.
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Watch the belt carry charge into the dome. See how deposited charge immediately rushes to the outer surface. Bring a grounding sphere close to trigger a spark! Toggle the field view to see why charge can’t stay inside: E = 0 in the interior.
E = σ / ε₀
The field at a conductor’s surface depends only on how much charge is packed per unit area. Sharp points have high σ, creating intense fields that can ionize air and produce sparks.
Sharp metal points concentrate charge, creating intense fields that ionize air and provide a safe discharge path before lightning strikes the building.
Your car protects you in a lightning storm because charge stays on the outer metal surface. The interior field is zero — you’re in a Faraday cage.
In thunderstorms, charge concentrates on ships’ masts and airplane wingtips, ionizing the air into an eerie glowing plasma — St. Elmo’s fire.
Van de Graaff generators can reach millions of volts, and were among the first machines used to accelerate particles for nuclear physics experiments.
“Charge always finds its way to the surface. Sharp points concentrate it until the air itself breaks down. A Van de Graaff is just a clever way to keep pumping charge onto a dome that can’t hold it inside.”
Spark Machine
Build and run your own Van de Graaff generator. Control belt speed, dome size, and humidity. Bring a grounding sphere close to trigger spectacular sparks. Visualize the surface charge distribution and watch how sharp points change everything.
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Crank the belt speed to max and watch charge accumulate on the dome — notice it’s all on the outside. Bring the grounding sphere closer until a spark jumps. Now add a sharp point to the dome and watch: charge leaks away before a spark can form. Try changing dome size — bigger domes reach higher voltages because charge is spread over more area, keeping σ lower.
Charge on a conductor lives on the outer surface, with density highest at sharp points. E = σ/ε₀ at the surface means sharp points create enormous fields. When the field exceeds ~3 MV/m, air breaks down and you get a spark. That’s the whole story of lightning, Van de Graaff generators, and St. Elmo’s fire.