94 Week 2: Continuous Charge and Gauss’s Law
itinsideof a hollow, conducting sphere and touch it to the larger sphere on the inside. Charge is
immediately transferred and pushed to theoutsideof the larger sphere. The advantage of doing
this is that one can do it over and over again, accumulating an ever-larger charge on the larger
sphere! This is the basis of theVan de Graff generator illustrated in figure 27, which uses a
flexible (rubber or silk) belt to continuously conveytribolelectrically generated chargepicked
up from ground to a hollow conducting sphere at the top.
Triboelectric charge is charge that comes from rubbing two materials together and transferring
charge preferentially from one to another using simple friction (tribology in physics and engineering
is, recall, the study of friction) depending on the relativeelectronegativityof the materials being
rubbed together. By making the rollers of the e.g. rubber belt of different materials and/or physically
rubbing the rubber belt with a soft material, one can generate a charge on the rubber at the bottom,
push it up on theinsulatingbelt through a hole in the top spherical conductor on the belt, and pull
it off near the top roller with a plate covered with sharp points near the belt via thecorona effect
discussed in the chapter on dielectrics and capacitance.
Inside, a wire transfers it to the sphere, where it immediately movesto the outside surface of the
sphere. One has to push further charge up through the hole against the force exerted by the charge
already on the sphere, so the motor at the bottom has todo workin order to increase or maintain
the charge on the sphere.
Van de Graff generators were the basis of the very first “atom smashing” particle accelerators
used to probe nuclear structure. They are still in use today in research accelerators^38 They were
quickly largely replaced by e.g. cyclotrons – described elsewhere in this text – and other accelerators
capable of achieving more than the 1-30 MeV particle energies they can produce. While Van de
Graff generators were for a time used or considered for the productions of nucleotides used in nuclear
medicine, I was able to find no real evidence that they are currentlyin an sort of medical production
environment. The much more compact cyclotron, on the other hand, has almost become a standard
piece of hospital equipment, because many of the most useful isotopes have very short half-lives
(deliberately!) and hence have to be produced right next to where they will be used (as close as
“down the hall”) in order for the isotopes not to decay below usefullevels during the time required
for transportation.
(^38) Duke University has a high-resolution tandem Van de Graff accelerator as of the time of this writing – I helped
to design its beam optics as a project in my senior year at Dukeas an undergraduate.