| DESCRIPTION:
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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