Charges and devices

1. The Faraday ice-pail experiment

This experiment shows an important result is electrostatics.

Neither an electric field nor a volume charge density exists inside a conductor under static conditions .

Inside a charge conductor, there is no electric field, and there is no charge. The excess of charge reside always on the outside surface of the conductor. We use the Faraday ice-pail experiment and Gauss's law to find this result.



The Faraday ice-pail experiment contains a charged metal sphere lowered into a neutral metal bucket on an insulating stand. We use an electrometer, the device that measures charge to indicate the presence of charge outside the bucket.

If we hang a charged metal sphere inside a closed metal can, the bucket becomes charged as the sphere is lowered.

Once the bucket encloses completely the sphere and tilted, the sphere touches the inside of the can. The sphere loses its charge and the electrometer reading is unaffected; that is the outside of the can has a charge equal to the original charge on the sphere.



At each point along the chosen gaussian surface the electric field E is zero. The charge enclosed is then zero. That is the charge on the inner surface of the bucket is equal and opposite the charge on the sphere. Since the bucket is neutral, the charge on its outer surface is equal to the charge of the sphere.

2. The Van de Graaff generator

The Van de Graaff generator contains an electric motor at the base that drives a plastic pulley which drives A rubber belt.As the plastic pulley rotates, hence it acquires a negative charge from the rubber belt by triboelectrification that is a rolling contact between two different materials.

Therefore, the inside surface of the rubber belt becomes negatively charged. By induction, the outside of the belt becomes positively charged.

A conducting brush called the charge-spray-comb, at the base of the pulley drains the negative charges on the outside of the belt to ground. At the top of the rubber belt, the metal pulley is connected to a second charge-spray comb which is connected to the collector which is the outer metal sphere.

The collection of positive charge continues while the belt is being driven. At the outer metal sphere of radius R, the positive free charge Q is uniformly distributed, and the electrostatic potential is Q/4πε_oR.

As the generator continues to produce charge on the sphere, the related potential difference between the sphere and the ground can reach some million volts. While the charge is accumulated,the air around the sphere becomes ionized. Charging continues until a voltage break down occurs in the air, that results in an arc between the sphere and the ground.

We use also a ground sphere, positioned few inches away from the Van de Graaff dome metal sphere, and grounded to the base of the Van de Graaff. While the dome is charging, the ground sphere becomes charged, by induction, with an opposite sign charge. Note that we can reverse the charge of the sphere by simply reversing the two pulleys.

When the dome becomes enough charged, the ground sphere is attracted to the dome and a spark occurs. After the spark, the two spheres lose their charges.