W9_parallel_resonance.eps

50 Week 1: Discrete Charge and the Electrostatic Field

Homework for Week 1

Note well that there are “no numbers” in the following problems. Most problems are for “all
students of physics”. Some problems are marked with a * as “advanced” and are intended to be
assigned primarily to physics majors or engineering students, who are expected to know and use
a bit more calculus than life science students, but note well that there isplenty of calculus in
the general problems! It is impossible to learn and understand physics without calculus; Newton
invented calculusjust so he could formulate physicsand this courseteachesthe correct use of algebra,
geometry, trigonometry, calculus in general including simple differential equations (e.g. the harmonic
oscillator, the wave equation) in the solving of problems.

Problem 1.

Physics Concepts

In order to solve the following physics problems for homework, you will need to have the following
physics and math concepts first at hand, then in your long term memory, ready to bring to bear
whenever they are needed. Every week (or day, in a summer course) there will be new ones.

To get them there efficiently, you will need to carefully organize whatyou learn as you go along.
This organized summary will be astandard, graded part of every homework assignment!

Your homework will be graded in twoequalparts. Ten points will be given for a complete
crossreferenced summary of the physics concepts used in each of the assigned problems. One problem
will be selected for grading in detail – usually one that well-exemplifies the material covered that
week – for ten more points.

Points will be taken off for egregiously missing concepts or omitted problems in the concept
summary. Don’t just name the concepts; if there is an equation and/or diagram associated with the
concept, put that down too. Indicate (by number) all of the homework problems where a concept
was used.

This concept summary will eventually help you prioritize your study and become your own
personal study guide to review for exams! To help you understandwhat I have in mind, I’m
building you a list of the concepts forthisweek, and indicating the problems that (will) need them:

• Coulomb’s Law:
  F~ij=keqiqj(~ri−~rj)
  |~ri−~rj|^3
  (withke= 9× 109 N-m^2 /C^2 ). Needed in problem(s) 4, 5, 6, 7, 8, 9, 10, 11. A core concept!


• Electric Field:
  E~= lim
  q 0 → 0

F~ 0

q 0

=

keq(~r 0 −~r)

|~r 0 −~r|^3

or of a point charge, located at the origin:

E~=keq

r^2

rˆ

Needed in nearly all of the problems.

• This definition ensures that we can find the force on a charge as follows:

F~=qE~