# Van De Graaf Generator & Gauss's Law

• matangi7
In summary, a Van de Graff generator uses Gauss's law to keep charges from accumulating on the inside of a conducting shell.
matangi7
My Textbook states"The same principle behind Faraday’s ice pail experiment is used in a Van de Graaff electrostatic generator (Fig. 22.26). A charged belt continuously carries charge to the inside of a conducting shell. By Gauss’s law, there can never be any charge on the inner surface of this shell, so the charge is immediately carried away to the outside surface of the shell."
How is Gauss's law relevant to the Van De Graaf Generator? Doesn't the situation have to be electrostatic to apply Gauss's law? Doesn't a Van De Graaf Machine have a current flowing, not static charges? Attached is the diagram in my textbook.

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The machine that is shown will continue to carry charges to the dome until such time as the accumulated charge will create a potential difference with the surrounding air as to cause coronal discharges or full breakdown of the air with a discharge to ground.reducing the net charge on the sphere. When used as a charged particle accelerator the dome is connected to its base by a string of very high resistance resistors to bleed off charge along with the particle beam while the charge deposited on the belt is carefully regulated to maintain the desired potential on the dome.

The Van de Graff generator is actually a demonstration of Gauss law. The fact that no charge is present inside the surface of the shell ( in this case, it is the inner surface of the shell) is one of the results of gauss law. Here's a link to the derivation of how no charge exists inside a shell: https://ucscphysicsdemo.wordpress.c...lectric-field-inside-and-outside-of-a-sphere/
And gauss law can be applied to moving charges too, but also then, in the case of the van de graff generator, the charges are only transferred via the charged belt and distributed on the outer surface of the shell and cannot really be called "moving charges". Also, there is no "current " flowing, its just static electricity.

## 1. What is a Van De Graaf Generator?

A Van De Graaf Generator is a device used to generate static electricity. It consists of a large, hollow metal sphere connected to a rubber belt that rotates on pulleys. As the belt moves, it rubs against the metal sphere, creating static electricity on the surface of the sphere.

## 2. How does a Van De Graaf Generator work?

A Van De Graaf Generator works by using the principle of electrostatic induction. As the belt rubs against the metal sphere, it transfers electrons from the sphere to the belt, creating a positive charge on the sphere. This charge continues to build up until it reaches a high enough voltage to create a spark or discharge.

## 3. What is Gauss's Law?

Gauss's Law is a fundamental principle in electromagnetism that describes the relationship between electric charge and electric fields. It states that the electric flux through a closed surface is equal to the total charge enclosed by that surface divided by the permittivity of the surrounding medium.

## 4. How is Gauss's Law related to Van De Graaf Generator?

Gauss's Law is essential for understanding how a Van De Graaf Generator works. It helps explain the buildup of electric charge on the surface of the metal sphere and the resulting electric field. It also helps calculate the maximum potential difference that can be achieved by the Van De Graaf Generator.

## 5. What are the practical applications of Van De Graaf Generator & Gauss's Law?

Van De Graaf Generators have various practical applications, including particle accelerators, nuclear research, and medical equipment. Gauss's Law is also used in many technologies, such as capacitors, electric motors, and generators. It is also crucial in understanding the behavior of lightning and designing lightning protection systems.

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