Download exam i, physics 1306

EXAM II, PHYSICS 2401, November 1, 2010, 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!
 -Q
a. State Coulomb’s Law.
b. State Gauss’s Law.
c. Briefly Define the following terms: i) Electric Field, ii) Electric Potential.
iii) Electric Flux, iv) Capacitance.
d. See Figure 1. A positive point charge q is initially placed at the center of a
non-conducting circular ring carrying a uniformly distributed negative
Fig. 1
charge –Q, as shown. 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 the figure) in either direction. There will
now be a net force on q. Will that force be directed back towards the ring center or away
from it? WHY?? Explain your answer!!
e. See Figure 2. Consider two parallel, charged, conducting plates, a distance d = 0.04 m
apart, as in the figure. The top plate has a net
positive charge and the bottom plate has a net

negative charge of the same magnitude. The
|
Fig. 2
points A, B, C, and D represent points in
d
space (not charges). Points A, C and D are

each a distance 0.01m from the nearest plate.
Point B is halfway in between the two plates.
Rank the potential differences VAB, VAC, VAD and VBC from greatest to least.
Explain your ranking!!
NOTE: WORK ANY TWO (2) OF PROBLEMS 2., 3., 4., or 5.!!!!!
2.
Figure 3 shows two point charges Q1 = - 30 μC & Q2 = 45 μC separated by distance d =
15 cm. (d = r1 + r2 in the figure) Consider
Fig. 3
the point P in the figure, a distance r1 = 3
cm from Q1.
a. Calculate the magnitude and direction of the total electric field at point P.
b. Calculate the total electric potential at point P.
Suppose that an electron (charge q = -e = -1.6  10-19 C, mass m = 9.1  10-31 kg) is placed at point P.
c. Calculate the magnitude and direction of the total force on the electron (excluding gravity) at
point P. What Physical Principle (or Law) did you use to do this calculation?
d. Calculate the electric potential energy of the electron at point P.
e. If the electron is released at point P, calculate the magnitude and direction of the initial
acceleration it experiences due to the force you calculated in part c. What Physical Principle (or
Law) did you use to do this calculation?
3.
Figure 4 shows two point charges, Q1 = -50 μC and Q2 = 50 μC placed
along the x-axis. Q1 is 26 cm to the right of the origin. Q2 is 26 cm to
the left of it. Consider the point A in the figure, which is at a distance of
30 cm in the y-direction from Q2 (so, it’s distance from Q1 is 60 cm).
At point A calculate:
a. The x-component Ex1 of the electric field due to Q1 and the xcomponent 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 (φ in the figure) of the total electric
field due to Q1 and Q2.
e. The total electric potential due to Q1 and Q2.
NOTE: WORK ANY TWO (2) OF PROBLEMS 2., 3., 4., or 5.!!!!!
4.
Fig. 4
NOTE: WORK ANY TWO (2) OF PROBLEMS 2., 3., 4., 5.!!!!!
Figure 5 shows a non-conducting sphere of radius r0, which contains
a positive charge Q that is uniformly distributed throughout it’s
volume. Calculate:
a. The electric field outside the sphere (r > r0).
b. The electric field inside the sphere (r < r0).
c. The electric potential outside the sphere. (r > r0)
d. The electric potential inside the sphere (r < r0).
Fig. 5
e.
Now consider a different situation in which the charge Q is not
uniformly distributed throughout the sphere, but instead has volume charge density varying with
distance r from the center of the sphere as ρE = Ar, (A is a constant). Repeat the calculation of
part b for the electric field inside the sphere (r < r0).
The following may be needed: Differential volume element in spherical coordinates (with no angular
dependence): dV = 4πr2dr. Integral of r to a power ∫rndr = [rn+1/(n+1)] (n ≠ -1).
5.
NOTE: WORK ANY TWO (2) OF PROBLEMS 2., 3., 4., 5.!!!!!
Figure 6 shows a cylindrical capacitor of length ℓ, with an inner conductor of radius Rb surrounded
by a coaxial conductor of radius Ra. A charge –Q is uniformly
distributed on the surface of the outer conductor and a charge Q is
uniformly distributed on the inner conductor. Calculate:
a. The electric field between the conductors (Rb < r < Ra).
b. The electric potential between the conductors (Rb < r < Ra).
c. The capacitance of this capacitor if the space between the
conductors is vacuum. Repeat this calculation if that space is filled
with a dielectric of dielectric constant K.
Fig. 6
F