W9_parallel_resonance.eps

Week 2: Continuous Charge and Gauss’s Law 95

Homework for Week 2

Problem 1.

Physics Concepts

Make this week’s physics concepts summary as you work all of the problems in this week’s
assignment. Be sure to cross-reference each concept in the summary to the problem(s) they were
key to. Do the work carefully enough that you can (after it has been handed in and graded) punch
it and add it to a three ring binder for review and study come finals!

Problem 2.

x

λ

θ 1 θ 2

y

x 1 x 2

A uniform line of charge with charge per unit lengthλ 0 runs fromx 1 tox 2 (wherex 1 < x 2 by
convention) on thexaxis. Findboth componentsof the electric field at an arbitrary pointyon the
yaxis. Note thatx 1 andx 2 are arbitrary aside from their ordering, so your answer should make
sense for e.gx 1 <0 andx 1 >0.

Note that this problem isworked for youas anexampleboth in class and in the text. Why, then,
you might ask yourself, is it also on the homework? Many of the examples worked in class or the
text are very nearly theonlyproblems of their type that can be sanely solved by e.g. integration
by ordinary mortal humans. Youwill not learn it from just seeing me present it, or reading its
presentation in a textbook. You mustdo it yourself– ideally enough times and carefully enough to
be able to do it yourselfwithout looking back at the solution, easily– in order to learn this problem
and the ideas it archetypically represents and make it/them your own.

All problems that are presented in lecture, in the textbook,and as homework prob-
lems are extremely likely to show up as quiz or exam problems!In some cases, “extremely
likely” meanscertain. In a subset of those cases I might even tell you that it is certain. But re-
gardless, agood studentwillalways be able to solve every homework problem perfectly, without
looking, by exam time. Anexcellent student– one who deserves an A in the course – will be
able toexplain what they are doing as they do so (for example, to other members of their study
group) and will be able to handle minor variations that make the problem not quite identical to the
lecture/text/homework it is based on.

Just something to keep in mind while working on these problems in groups. The homework in
this textbook is (unlike that of many textbooks) carefully designedto direct your study activities to
where they will pay off. The “gold standard of learning” is being able toarticulate your solutions
well enough that you could teach a novice how to solve every problemof your homework a month