The Van de Graaff Generator

Have you ever visited a science museum? If so, you probably saw a metal ball that causes spectators' hair to stand on end, or perhaps create small lightning shows. That is a Van de Graaff generator, a device invented in 1929 which generates electrostatic forces to create high voltage DC current. They are also commonly used as particle accelerators for physics research and nuclear medicine, to generate high energy particles and x-ray beams.

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Electrostatic equilibrium occurs in a conductive material when there is no net motion of charge within it. The electric field is zero everywhere inside an insulated conductor. The electrical field on the outside of the conductor will be perpendicular to its surface. This must be the case, since if a field were present in the material itself, any free charge would flow and the conductor would no longer be in equilibrium. Any excess charge is present only on the surface, tending to accumulate near the sharpest points of curvature. In a Van de Graaff generator, these principles are utilized to do work.

A rotating rubber belt turns over two rollers of differing substance(often acrylic and metal), leaving the surface of the belt charged. A motor or hand-crank moves the belt past wires called combs, which serves to deliver positive charge to the structure's dome, which is a hollow metal globe on an insulated column. Negative charge is repelled from the dome and attracted to ground potential through the lower comb. Eventually, the potential difference between the positive globe and negative ground grows very high, and electrical discharge occurs.

The Van de Graaff generator was developed by Robert Van de Graff as a particle accelerator for research. Subatomic particles can be accelerated to incredible speeds in a vacuum tube by the high electrical potentials achieved by the device. Often this is achieved by injecting negative ions into the machine, which are attracted to the positive terminal and stripped of electrons. Now positively charged, the ions are repulsed by the terminal at high speed.Until the development of the cyclotron, Van de Graaff's invention was the most powerful accelerator available. While an open-air device can usually achieve voltage of no more than 5 million volts, when enclosed in pressurized gases, potentials of 25 megavolts can be achieved. (A megavolt is a million volts.)

The magnitude of an electrical field E multipled by the area of the surface perpendicular to it A gives us the electric flux (theta).

Gauss' law tells us that electrical flux through any closed surface equals the charge inside the surface divided by
the permittivity of free space, ε0 = 8.854187817...×10−12 F⋅m−1 (farads per meter).

Gauss' Law is one of Maxwell's Four Equations, which form the basis of classical electrodynamics.