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

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Published on 12 Oct 2018

Department

Physics

Course

PHYSICS 209

Professor

PHYSICS 209

MIDTERM EXAM

STUDY GUIDE

Fall 2018

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 aiaj≥0,(2)

for all vectors a, with equality if and only if a= 0. Show that Cij is positive deﬁnite.

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find more resources at oneclass.com

– 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.

find more resources at oneclass.com

find more resources at oneclass.com