EXAM I, PHYSICS 2401, February 18, 2013, Dr. Charles W. Myles
INSTRUCTIONS: Please read ALL of these before doing anything else!!!
1. PLEASE put your name on every sheet of paper you use and write on one side of the paper
only!! PLEASE DO NOT write on the exam sheets, there will not be room! This wastes
paper, but it makes my grading easier!
2. PLEASE show all work, writing the essential steps in the solutions. Write formulas first, then
put in numbers. Partial credit will be LIBERAL, provided that essential work is shown.
Organized, logical, easy to follow work will receive more credit than disorganized work.
3. The setup (PHYSICS) of a problem will count more heavily than the math of working it out.
4. PLEASE write neatly. Before handing in your solutions, PLEASE: a) number the pages &
put the pages in numerical order, b) put the problem solutions in numerical order, & c)
clearly mark your final answers. If I can’t read or find your answer, you can't expect me to
give it the credit it deserves.
5. NOTE!! The words “EXPLAIN”, “DISCUSS” & “DEFINE” below mean to answer mostly
in ENGLISH, NOT math symbols!
Constants that may be needed:
Permittivity of free space: ε0 = 8.85  10-12 C2/(N m2). k = [1/(4πε0) = 9.0  109 N m2/C2]
NOTE: PLEASE HELP ME GRADE EFFICIENTLY BY FOLLOWING
THE ABOVE SIMPLE INSTRUCTIONS!!! FAILURE TO FOLLOW
THEM MAY RESULT IN A LOWER GRADE!! THANK YOU!!
An 8.5’’ x 11’’ piece of paper with anything written on it & a calculator are allowed. NOTE:
Question 1, Conceptual Questions IS REQUIRED! You may work any two (2) of the
remaining problems for three (3) problems total. Question 1 is worth 34 points. The others are
equally weighted & worth 33 points, for 100 points on this exam.
1. MANDATORY CONCEPTUAL QUESTIONS!!! Answer briefly all parts in a few
complete, grammatically correct English sentences. I want answers which use mainly
ENGLISH WORDS, NOT symbols or equations! If you insist on using symbols, DEFINE
all symbols you use! NO credit will be given for answers with ONLY symbols! Answer parts
a and b in English, NOT with formulas!
a. State Coulomb’s Law.
b. State Gauss’s Law.
c. Briefly Define the following terms: i) Electric Field, ii) Electric Flux, iii) Electric
Potential Energy, iv) Electric Potential.
d. See Fig. 1. A positive point charge q is initially placed so that it is
inside a tiny hole in the center of a non-conducting circular disk of
radius R carrying a uniformly distributed negative charge -Q, as
 -Q
shown (q isn’t shown in the figure). In that position, by symmetry, q
is in equilibrium with zero net force on it. However, now consider the
situation if q is moved a small distance x along the ring axis (x-axis in
Fig. 1
the figure) in either direction. There will now be a net force on q.
Will that force be directed back towards the disk center or away from
it? WHY?? Explain your answer!!
e. See Fig. 2. The figure is a square of side d. Two point charges, Q
and 2Q are placed on two adjacent corners of the square a
distance d apart. Point D is on that same side of the square,
Fig. 2
halfway between the two charges. The other two corners of the
square are labeled A and B so that line AB is also of length d.
Point C is at the center of the square. Assume that the electric
potential is defined such that V = 0 at r  . Rank the electric
potentials at the four points VA, VB, VC, and VD from largest to
smallest. Explain your answer!!
NOTE: WORK ANY TWO (2) OF PROBLEMS 2., 3., or 4!!!!!
2.
Fig. 3 shows two positive point charges Q1 = 2.0 μC, Q2 = 1.0 μC
1.00 μC
and a proton with charge q = |e| = 1.6  10-19 C arranged along the
x-axis. The larger charges are 1.6 m apart & are placed
symmetrically, such that they each are 0.8 m from the origin. The
proton is placed at the origin. Calculate (find numerical values for) the following:
Fig. 3
a. The magnitude and direction of the total force that the charges Q1 & Q2
exert on the proton at the origin. What Physical Principle (or Law) did you use to do
this calculation?
b. The magnitude and direction of the total electric field at the origin due to Q1 & Q2 .
c. The total electric potential at the origin due due to Q1 & Q2.
d. The electric potential energy of the proton at the origin.
Initially, the charges are fixed at the positions in the figure. Suppose that now the proton at
the origin is released from rest at while the two larger charges are held fixed at their positions
in the figure.
e. Calculate (find numerical values for) the magnitude and direction of the acceleration
the proton experiences due to the force you calculated in part a. (Proton mass m = 1.67  10-27 kg)
What Physical Principle (or Law) did you use to do this calculation?
NOTE: WORK ANY TWO (2) OF PROBLEMS 2., 3., or 4.!!!!!
3.
Q3
Fig. 4 shows three point charges, Q1 = 2.0 μC, Q2 = -4.0 μC, Q3 = 7.0 μC
Fig. 4
located at the corners of an equilateral triangle of side length 0.50 m. Q1 is
at the origin, Q2 is on the x-axis at x = 0.50 m & Q3 at the top vertex of
the triangle as shown. At the position of the charge Q3 = 7.0 μC,
calculate (find numerical values for):
Q2
a. The x-component Ex1 of the electric field due to Q1 and the xQ1
component Ex2 of the electric field due to Q2.
b. The y-component Ey1 of the electric field due to Q1 and the ycomponent Ey2 of the electric field due to Q2.
c. The x-component Ex and the y- component Ey of the total electric field due to Q1 and Q2.
d. The magnitude and direction of the total electric field due to Q1 and Q2 and the
magnitude and direction of the total force on Q3 due to Q1 and Q2.
e. The total electric potential due to Q1 and Q2.
Fig. 5
NOTE: WORK ANY TWO (2) OF PROBLEMS 2., 3., 4.!!!!!
4. Fig. 5 shows a cross section of a portion of an infinitely long, nonconducting CYLINDER of radius R0 which has a which has a
positive uniform volume charge density ρ. (Hint: The only way I
know to do this problem is to use Gauss’s Law!). Calculate (in
terms of the variables of the problem):
a. The electric field everywhere outside the cylinder (r > R0).
b. The electric field everywhere inside the cylinder (r < R0).
c. The electric potential everywhere outside the cylinder. (r > R0)
d. The electric potential everywhere inside the cylinder (r < R0).
Some information about a cylinder of radius r & length ℓ that might be useful:
Lateral surface area: A = 2πrℓ. Volume: V = πr2ℓ. Differential volume element: dV = 2πℓrdr
These integrals might be useful: ∫rn dr = (rn+1)/(n+1); n is any power (n  -1).
∫(dr/r) = ∫r-1dr = ln(r)
Don’t forget the lower limits!!!