Physics 6346, Electromagnetic Theory I
Fall 2000
Homework 2
Due Friday, September 8, 5:00 p.m.
Reading:
Read Ch. 1 (again).
1.
Potential for the hydrogen atom.
This is essentially
Jackson
1.5 done in reverse.
Start with the time averaged electron charge density
ρ
(
r
)=

q
α
3
8
π
e

αr
,
(1)
and a point charge
q
at the origin, compute the electric ﬁeld using Gauss’s law, and
then ﬁnd Φ(
r
) by integration. You should ﬁnd Jackson’s Φ(
r
).
What is the numerical magnitude of
E
at the typical atomic distance of 1
˚
A?
2.
Charged ring.
A circular ring of radius
R
carries a uniformly distributed charge
q
.
The ring is centered at the origin of the
x

y
plane, so that the
z
axis is the symmetry
axis.
(a) Find the electrostatic potential on the
z
axis of the ring.
(b) Find the potential at any point in space. You can express the integral as an elliptic
integral or a hypergeometric function, or as an expansion in Legendre functions
(see
Jackson
, p. 91).
(c) A positive test charge is located at the center of the ring. Is this a position of
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 Fall '08
 Staff
 Electron, Charge, Work, Fundamental physics concepts, charge density

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