ANSWER: Start with no charge, then bring successive bits in to add
uniformly to the charge
of the shell. A given bit of charge
acquires an electrostatic potential energy
in the process. Thus the total energy
required to assemble the
shell is
. If we set
this equal to
we get
or
.
The
Compton wavelength of the electron
is twice as big,
fm, where "fm" stands for
"femtometers" or "fermis" (named after Enrico Fermi);
both are the same as
m.
ANSWER: The original capacitance was . The capacitor with
the insert as shown is equivalent to two identical capacitors in
series, each of which has a gap of
between its plates,
so that
. The equivalent capacitance of two
capacitors in series is given by
. Thus
.
The battery supplies
V. The capacitances are
F,
F,
F and
F.