Week 2: Continuous Charge and Gauss’s Law 93
Second (b) a charged object (perhaps prepared by the triboelectric effect, rubbing a glass rod
with silk to produce the negative charge shown or using a crude electrostatic generator) is brought
near the conductor. There it attracts charge of the opposite sign and repels charge of the same sign
which tries to get as far away as possible, which happens to be the ground.
Third (c) the connection to ground is removed, isolating the chargeon the sphere, and the
induction charge is removed, producing:
(d) a charged, isolated conducting sphere.−q
+++
++
−− ++
−
−−
−−
−(a) (b)
−−
−
−
−
−
−
++
+++++−Q +Q
Figure 26: Charging by induction with no ground.It is not strictly necessary to use the ground. You can also produce equal and opposite charges by
using two spheres connected with a wire, bringing the charged object near one and pushing charge
over to the other before disconnecting the wire as before. This is schematically illustrated in figure
26 above. Since the two objects began electrically neutral, they willhave equal and opposite charges!
To produce thesamecharge on two identical conducting spheres, it suffices to charge one sphere
up as shown in figures 25 or 25 and then bring it into contact with an identical sphere. The charge
then splits onto the two spheres symmetrically, leaving them both with half of the original charge.
This process can be repeated with more spheres, producing a series of spheres withQ,Q/2,Q/4,
Q/8 on them. This suffices to be able to demonstrate the needed bilinearity in charge in Coulomb’s
Law, provided only that one can measure very small forces and distances with some accuracy.
++
+
+friction charge transfer
corona
effectcharged conducting sphere
(electrode)
transfer
rubber beltmotor
Figure 27: A Van de Graff Electrostatic GeneratorFinally, it is possible to charge up a conducting sphere at the end of aninsulating rod and move