Physics 42 Homework
From Tipler, 5th edition
Instructions: Do all assigned problems. Please try to use the
Method of Three
Passes
, attached. Read over this for other general comments and instructions
in any event.
Note that bonus questions have to be solved
without the direct help
of Kristine
or me. You may still work in groups, you can solve them with discussion on the
class list (where Kristine or I
might
reply to help out the entire class with our
answers), you can ask other faculty or graduate students, you can look online or
in other texts or in the library for solutions, but
you
have to build your problem
solving skills and confidence by attacking them. They are often worth quite a
lot of credit!
Chapter 21:
41,47,56,61,62,72,78,81,85
Chapter 22:
29,47,50,56,61,66,77,88,92,93,94
Chapter 23:
16,59,73,85,87,88,89,90,91,92,93.
Bonus questions, worth three points each:
Find the potential of an electric dipole at an arbitrary point in space as
follows. Put
±
q
at
±
a/
2 on the
z
axis. Pick a point
r
= (
r, θ, φ
= 0) (the
latter just means “in the plane of your picture). Write down the potential
at that point.
This is your answer.
Now let
r
≫
a
.
Do a binomial
expansion of both denominators, set
p
a
=
qa
, and tell me the
potential of
a point dipole
at an arbitrary point in space relative to the dipole axis.
Pretty cool!
This is a really important thing to understand – just ask
Kristine!
Problem 95. When you solve this you are actually deriving an important
theorem that says that the potential at any point in space that is free
from charge is the average over a spherical surface around that point. A
related theorem tells you that both the maximum and minimum potential
inside any chargefree volume must occur on the surface. Both of these
are consequences of Gauss’s Law expressed as the
Poisson equation
(the
inhomogeneous Laplace equation). You won’t learn all of this for several
years, but you’ll learn it much more
easily
then if you solve this problem
now, which isn’t
that
difficult!
Chapter 24: 51, 56, 57, 84, 92, 93, 94, 97, 104, 112
Bonus: Problem 110.
1
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Chapter 25: 30, 56, 57, 97, 116, 118, 133, 144, 145
Bonus. Suppose you have are handed a “infinite” flat piece of metal screen
ing consisting of thin wires in a rectangular mesh. Each bit of wire between
two adjacent intersections in the screen has a resistance
R
.
From symme
try,
find the
total
resistance between to adjacent intersections. Note that
this quantity is bound to be less than
R
because there are other pathways
that current can take between the interactions. Note also that if you try
to actually sum the resistance network, you’ll go mad. There’s a trick, so
think about it and see if you can figure it out.
This is an example of a problem where clear conceptual thinking can
sometimes do a problem that cannot, literally, be algebraically solved.
Give your left brain a rest and let your right brain drive. Visualize what
the currents and so on must be doing.
Think about superposition, and
boundary conditions at infinity on the mesh. Don’t think about series and
parallel sums.
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 Spring '11
 BROWN
 mechanics, Work, Kristine, straight cylindrical wire

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