PHYSICS 209 Study Guide - Fall 2018, Comprehensive Midterm Notes -

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Published on 12 Oct 2018
School
Berkeley
Department
Physics
Course
PHYSICS 209
Professor
PHYSICS 209
MIDTERM EXAM
STUDY GUIDE
Fall 2018
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Physics 209
Fall 2002
Homework 1
Due Saturday, September 7, 2002
Reading Assignment: By Saturday, August 31, you should have read Chapters 1 and 2
of Jackson. By Saturday, September 7, you should have read Chapters 3 and 4.
1. Jackson, 1.10 (mean value theorem).
2. Jackson, 2.1, part (f) only. In this problem, you are to quote only the numerical answer
(in electron volts). Do not present any of your calculations. However, I suggest you do the
calculation in whichever system of units you are less familiar with (probably Gaussian),
then convert the answer if necessary. Full credit for an answer within 10% of the correct
value; otherwise, no credit.
3. Jackson, problem 2.7.
4. Jackson, problem 2.10.
5. Let there be a set of conductors with surfaces, Si, i = 1,...,n. The conductors are not
in contact. Let voltages Vibe applied to the conductors. The voltages are measured with
respect to ground at infinity.
(a) Explain why the charges Qiare linear functions of the voltages Vi, that is, show that
there exists a matrix Cij such that
Qi=X
j
Cij Vj.(1)
Using Green’s reciprocation theorem (see Jackson problem 1.12) show that Cij =Cji.
(b) Apositive definite matrix Mij is a symmetric matrix such that if a= (a1,...,an) is a
vector, then
X
ij
Mij aiaj0,(2)
for all vectors a, with equality if and only if a= 0. Show that Cij is positive definite.
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– 2 –
(c) The usual case is n= 2. Express the usual capacitance Cof two conductors in terms
of the components of the 2 ×2 matrix Cij , and show that it is positive.
6. (Postponed to next week.) Jackson, problem 2.28.
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