Electromagnetic Theory I
Problem Set 3
Due: 12 September 2011
9. The formula for the total energy stored in a static electric Feld
U
= (
ǫ
0
/
2)
i
d
3
x
E
2
includes the selfenergy of the charges as well as their mutual potential energy. As discussed
in class the selfenergy of a point charge is inFnite. Study this issue for a single charge
Q
by spreading out a point charge in two di±erent ways: a) Replacing the point charge
by a uniformly charged spherical surface of radius
δ
and b) Replacing the point charge by
a uniformly charged ball of radius
δ
. In each case, Fnd the electric Feld everywhere and
evaluate the integral deFning
U
. Classical physics puts no apriori limit on how small
δ
could
be. However, relativistic quantum mechanics implies that a particle’s location cannot be
known within a distance smaller than its Compton wavelength
p
/mc
. ²or cases a) and b),
assume
δ
=
p
/mc
to get an estimate for the self energy of the electron.
10. The standard capacitor used in electrical circuits has only two conducting plates and is
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 Spring '08
 Staff
 Electron, Charge, Energy, Potential Energy, Electric charge

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