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MIT Physics 8.02 - Electricity & Magnetism

SECTION : Electrostatics      

SUBJECT: Charging a Van de Graff Generator (animation)  

This animation shows the process of charging a Van de Graff generator in the presence of a stationary positive point charge. The presence of that charge means that we have to do more work than we would normally have to do to charge up the generator. If the point charge above has charge q and the generator has radius a and is charged to a total charge Q, the energy we must putin to charge up the generator is:

This total amount of energy is stored in the electrostatic field surrounding the generator after it is charged. As we charge it, there is a Poynting flux outward from the region where we are creating electromagnetic energy. The region is where the charge is being moved against the electric field on the conveyer belt (inside the cylindrical shaft of the generator). This region is where the creation rate per unit volume for electromagnetic energy (-J dot E), is positive. Energy is created there and flows out to fill the space around the generator. This flow can be seen in the motion of the electric field lines, which is always in the direction of the Poynting flux.

After the generator is fully charged, we release the stationary positive charge sitting above it. In the case shown here, there is enough electrostatic repulsion to overcome gravity, and the charge moves upward. We can see that the source of its increasing kinetic energy and gravitationial potential energy is the electrostatic field, because again we see the flow of energy out of that field, as indicated by the motion of the electric field lines. Since we have no energy dissipation in the system, the charged particle will eventually come to rest at some distance above the generator, and then start to fall back, transferring gravitational potential energy and kinetic energy back into the electrostatic field as shown by the field line motion.





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