198
Chapt. 25
Electric Potential
the charge to flow to the dome. The charge can be positive (absence of electrons) or negative
(excess of electrons). We assume positive for definiteness in this problem.
a) Say the belt conveys a constant net current (charge per unit time) of
I
to the dome. What
is the formula for time
t
for charge on the dome to reach
q
when it started at zero?
b) Say the charge
q
ends up uniformly spread over the outer surface of the dome which we
can approximate to high accuracy as spherical shell of radius
R
. Let the radial coordinate
be
r
.
Assuming exact spherical symmetry, what are the formulae for the
ELECTRIC
FIELD
and
ELECTRICAL POTENTIAL
for
r
≥
R
?
HINT:
General formulae are
not acceptable answers. What are the formulae for this specific case.
c) The Van de Graaff generator is a neat trick to build up net charge. But in building up
net charge, one also builds up potential energy in the distribution of charge on the dome’s
surface. But you don’t get things for free. By what process done by what component of
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 Fall '06
 Buchler
 Physics, Charge, Current, Electric Potential, Electrostatics, Electric charge, 4 m, Dome

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