Physics 272: Advanced Honors Physics II
due in class Monday, January 29, 2018 [DRAFT:
more notes and answers to be added]
Reading: Purcell 1.7-1.11 and 1.13
the solution for each problem should be written on a
separate page (sorry, trees!) to facilitate the grading.
IN ADDITION, YOU MUST COMPLY WITH THE PROBLEM
SOLVING CHECKLIST (copy provided for your convenience
I have put the answers at the bottom of this page. You
can use them to check your own answers -- if they don't
agree, you know you need to go back and look for at
least one mistake.
1. *Purcell 1.52: Equilateral triangle
The possible tediousness of this problem should inspire
you to find ways to group the quantities together for
numerical evaluation and also to use symmetry (the face
that qB=qC allows you to determine the direction of the
force on charge A, and to relate the force on charge B
to the force on charge C)
2. **Purcell 1.54(a) Semicircle and wires
The physics in this problem is easy, but the challenge
is to draw the diagram correctly, use trigonometry, and
Taylor expand to get the length of segment B (you should
neglect the width of the wire even though the diagram in
the book shows it, so the charge on segment B will be
the length of segment B times lambda).
For your convenience, the Taylor expansion of tan
(theta+d theta) around theta is tan
(theta+d theta) = tan (theta) + d theta
/(cos theta)2 + ...
**Purcell 1.55 Field from a finite rod
Use symmetry to determine when a component of the E
field is zero (note that point B is under the midpoint
of the rod).
More trigonometry for setting up the integral for the
field at point B.
1.63 Sphere and cones
Compute the potential energy of
the charge -q and use
conservation of energy. For (b),
you have to compute the
potential energy of the charge
-q at the point of a cone. If
you set up the integral right it
is very easy (use the coordinate
along the cone that varies from
0 to L as the integration
through a cube
uses Gauss law
to know how to
(b), there are
two ways. One
way is to use
cooler way is
bigger cube of
1.69: Carved out sphere
1.76 Hydrogen atom
To evaluate the integral, you could use integration by
parts OR you could use a nice trick, based on the fact
that d(int exp(- a x) dx)/da = - int
x exp(- a x) dx and you know (or should
know) how to do int
exp(- a x) dx. To get int
exp(- a x) dx,
1.77 Electron jelly (E field of uniform sphere)
9. **Purcell 1.72 Plane and slab (Application of Gauss'
OPTIONAL 10. **Purcell
1.71 Intersecting sheets
This is an absolutely adorable application of Gauss'
law. Use what you know about the field of a sheet (that
it's constant on each side of the sheet) and symmetry of
the hexagonal arrangement.
CHECKLIST: to be checked for EACH AND EVERY
PROBLEM you hand in!
0. NEVER write only the answer. You need to show where it came
from and why it is right.
1. Check that you have
drawn at least one diagram and labelled it clearly. This might
involve copying the diagram from the problem statement and adding
extra labels, or making a diagram from scratch. Make it pretty
large to leave room for labels and make it readable. Quantities
from the statement of the problem should appear in the diagram.
2. Check that the
meanings of any symbols you have introduced yourself are clear.
First, if the symbol is a label in the diagram, make sure the
diagram makes its meaning clear. If not, or if it is not in the
diagram, write a short phrase to explain what the symbol
3. Check that all vector
quantities are written so that their vector character is clear. In
typesetting, boldface indicates a vector quantity. In a diagram,
if you draw an arrow to indicate the direction and write the
magnitude next to the arrow (this is how we draw force diagrams).
In handwriting, put an arrow over the quantity to show it is a
vector. Velocity is a vector, so write v with an arrow over it.
The x component of the velocity is not a vector, so do not put an
arrow over it. In a sum, you cannot add a vector to a number. In
an equation, you cannot have a vector on one side and a number on
the other side.
4. Check that each
statement clearly follows from the previous statement. (This is in
the same spirit as Checklist Item #0 - you can't state things
without showing where they came from).
5. Check that you have
stated the answer at the end of the solution. The answer should be
an equation in the form
desired quantity =
expression in terms of given quantities
You might be tempted to
save writing by just writing the right hand side, but it is best
practice to write the whole thing (this acts as a final check that
your expression is indeed for the quantity the problem asked for).
To make it clear that it
is the answer, PUT A BOX AROUND IT.
1. a) FA = 2.34 N, FB = FC = 1.96 N (really should be only 1 sig
fig); b) 6.75 x 105 N/C
3. EA = 1.85 x 104 N/C, EB = 2.04 x 104 N/C
4. a) v = Sqrt[(2R sigma q)/(epsilon0 m)], b) v = Sqrt[(2R sigma q)/(epsilon0 m)]
5. a) q/(6 epsilon0), b) q/(24 epsilon0)
6. EA = a rho / (6 epsilon0) upward, EB = 17 a rho/(54 epsilon0)
7. 0.323 e, 3.5 x 1011 N/C
8. r = a/2
9. (sigma - rho d + 2 rho x)/(2 epsilon0) for 0<x<d, (sigma + rho d)/(2 epsilon0) for
x>d, -(sigma + rho d)/(2
epsilon0) for x<d
10. Check your answer by adding up the fields from each of the
three sheets in each of the six regions