PH1120
Electricity and Magnetism
L. Colonna-Romano/T. Keil
Term B98
Study Guide #1
This is the first in a series of four Study Guides that have been designed to help you get
the most out of this course. You will receive the others as the course progresses. The study
guides are built around a set of course objectives and include suggested study procedures and
problems to help you thoroughly understand those objectives. In addition, the homework
assignments are in the study guides. For many students, following the study guides closely
has proven to be an effective approach to successfully completing this course.
Vectors will be used throughout this course and it may be useful for you to review vectors
and operations involving vectors now. In particular, you should be familiar with the contents
of Secs. 1-8 through 1-10. (All references of this type may be found in the course textbook:
Hugh D. Young and Roger A. Freedman, University Physics, Addison-Wesley Pub. Co.,
c
Ninth Ed., 1996.)
Be certain that you can express a vector in î ĵ k̂-notation and also by
giving a magnitude and direction relative to some well-designated coordinate axes. Unit
vectors (Sec. 1-10) are sometimes confusing to students; be certain that you can calculate
the components of a unit vector parallel to a specified vector.
Objective 1
Coulomb’s Law
1) State Coulomb’s Law. (This means write it out in symbolic form and make sure you can
define each symbol used in the expression.
2) Given a set of point charges (two or more) at rest at specified locations, calculate the
resultant force (a vector quantity) on one of the charges caused by the other charge or
charges.
Suggested Study Procedures for Obj. 1
Read Secs. 22-1 through 22-4. Study carefully Sec. 22-5. This section contains two
important ideas: Coulomb’s law and the principle of superposition. The four examples are
important; you should be able to do similar problems. (When you study examples, I suggest
you do so by first observing the general approach to the problem and then working out all
the intermediate algebraic steps with pencil and paper.)
Suggested Problems for Obj. 1
1) In each case, determine the unit vector that is parallel to the two-dimensional vector
described below:
a) from (0, 0) to (0, 3)
b) from (0, 0) to (−4, 0)
c) from (0, 0) to (1, 1)
d) from (1, 2) to (3, −3)
e) from (1, 2) to (−2, −1)
2) Exercises: 22-6, 22-9, 22-13, 22-15.
3) Problems: 22-57, 22-62.
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Objective 2
Electric Field and Electric Flux
1)
2)
3)
4)
Define the electric field.
Calculate the electric field due to a set of point charges at rest at specified locations.
Determine the motion of a charged particle passing through an electric field.
Calculate the electric flux through a given surface.
Suggested Study Procedures for Obj. 2
Study Secs. 22-6 and 22-7 paying particular attention to Examples 22-5 through 22-9.
You should examine Examples 22-10 through 22-12 as we will refer to them later in the
course. Read Secs. 23-1 through 23-3.
Suggested Problems for Obj. 2
1) Exercises: 22-23, 22-25, 22-28, 22-29, 22-30, 22-32, 22-35, 22-36, 23-4.
2) Problem: 22-73.
Objective 3
Visualizing Electric Fields and Gauss’ Law
1) Sketch qualitatively the electric field associated with:
a single point charge of given polarity;
two or more stationary point charges of given relative magnitude and polarities;
a point charge or charges in the vicinity if a conducting surface.
2) Use Gauss’ Law to relate the electric flux through a closed surface to the charge contained
within that surface, and to the electric field along the same surface.
Suggested Study Procedures for Obj. 3
Study Sec. 22-8 and 23-4 through 23-6. All the example problems in these sections are
important.
Electric field lines form a useful way to picture how the electric field behaves in space.
The following is a set or rules for sketching electric field lines:
1) Field lines begin and end only on charges.
2) The number of lines beginning at a positive charge or ending at a negative charge is
proportional to the magnitude of the charge.
3) The direction of the field line is parallel to the direction of the force experienced by a
small positive charge at each point along the field line.
4) The number of field lines passing through an area of one square meter whose surface is
perpendicular to the lines (i.e., the density of field lines) is proportional to the magnitude
of the electric field.
5) No two field lines can cross.
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6) Under electrostatic conditions, field lines always meet the surface of a conductor perpendicularly; under electrostatic conditions, no field lines penetrate a conductor.
Suggested Problems for Obj. 3
1) Sketch the electric-field diagrams for each of the configurations in Fig. 1.
d)
a)
b)
+q
-q
+q
c)
(conductor)
3q
-q
-2q
(conductor)
-q
Fig. 1. Configurations for Suggested Problem 1, Objective 3.
2) Exercises: 23-10, 23-16, 23-26.
Homework
The homework assignments are an important part of this course and overall will count
for 10% of your final grade. Students are free to discuss the homework problems among
themselves, however, each student should write up his or her own individual solution for
submission. Blatant copying of the work of another student is unlikely to help you understand
the material.
Please note that because of the limited number of homework problems that you will
be submitting for grading, it is important that you also attempt as many of the suggested
problems as possible. Although the suggested problems are not to be turned in for grading,
they are equally important as the assigned homework in mastering the course objectives.
Solutions for assigned and suggested problems are posted.
Homework solutions are due at the beginning of your assigned lecture on the due date.
Late homework is accepted only in extraordinary circumstances.
Homework Assignment #1 due Friday, October 30, 1998
~ = 3.00 cm î + 2.50 cm ĵ and B
~ = −3.50 cm î − 1.00 cm ĵ,
Prob. 1-1. Given the vectors A
~ and B,
~ b) the angle B
~ makes with the positive x-axis, c) a
calculate a) the magnitudes of A
~ and d) a unit vector in the same direction as A
~ + B.
~
unit vector in the same direction as A,
Prob. 1-2. a) Two charged bodies exert a force of 40.0 mN on each other. What will the
force be if they are moved so that they are only one-eighth as far apart?
b) How close must two electrons be if the electric force between them is equal to the
weight of one electron at the earth’s surface?
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Prob. 1-3.
A small charge of 3.00 × 10−6 C is located at the point x = 2.00 m and
y = 3.00 m in the x-y plane. A second small charge of −2.00 × 10−6 C is at the point
x = 4.00 m and y = −1.00 m.
a) Draw a diagram showing the two point charges in the x-y plane.
b) Calculate the force that the first charge exerts on the second. Express your answer in
î ĵ-notation. Show this force in your diagram.
c) Calculate the force that the second charge exerts on the first charge.
Homework Assignment #2 due Monday, November 2, 1998
Prob. 2-1. Two point charges are placed on the x-axis as follows: charge q1 = 1.00 µC is
located at x = −0.200 m, and charge q2 = 5.00 µC is at x = 0.600 m. What is the magnitude
and direction of the total force exerted by these two charges on a charge q3 = 4.00µC located
at the origin?
Prob. 2-2. Four point charges are placed at the corners of a rectangle as shown in Fig. 2.
The magnitude of each charge is q = 1.20 µC and the sign of each charge is as shown in the
figure. If L = 1.200 m and W = 0.800 m, what is the electric field at the position of the
charge located at the lower left corner of the rectangle? What is the force exerted on the
charge at this position?
y
-q
-q
W
q
q
x
L
Fig. 2. Prob. 2-2.
Prob. 2-3. An electron is injected into the region of space between two horizontal parallel
plates 3.00 cm long with a velocity of 2.40 × 106 m/s directed 10◦ above the horizontal. The
magnitude of the uniform electric field between the plates is 1000 N/C directed upward as
shown in Fig. 3.
a)
b)
c)
d)
Find the maximum distance the electron rises above its initial elevation.
After what horizontal distance does the electron return to its initial elevation?
How much time does the electron spend between the plates?
If the electron is injected midway between the plates, what is the minimum plate separation if the electron is to avoid hitting the plates?
e) Sketch the trajectory of the electron.
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y
v
E
x
3.00 cm
Fig. 3. Prob. 2-3.
Homework Assignment #3 due Wednesday, November 4, 1998
Prob. 3-1. A point charge, q1 = 3.00 nC, is placed at x = −2.00 cm, y = 0 and a second
point charge, q2 = −3.00 nC, is placed at x = 3.00 cm, y = 2.00 cm.
a) Compute the electric field at the point x = 1.00 cm, y = −1.00 cm due to the two point
charges.
b) If a proton were to be placed at x = 1.00 cm, y = −1.0 cm, what force would the other
two charges exert on it?
Prob. 3-2. Three point charges of equal magnitude are evenly spaced along a vertical
axis; the outer charges are positive, the central one, negative. a) Sketch the electric field
lines due to this configuration of charges. b) Where is the electric field zero? You need not
work the algebra out completely but at least write an equation that would allow you to solve
for the zero-field locations in terms of L, the distance between consecutive charges. Explain
your reasoning; be sure to discuss the symmetry of the problem.
Prob. 3-3.
A cube is placed in a three-dimensional coordinate system with an edge
(L = 4.00 cm) along each of the three positive axes. There exists a uniform electric field
~ = −1.30 N/C î + 3.10 N/C ĵ. Find the electric flux through
everywhere in space given by E
each of the six faces of the cube and the total electric flux through the entire cube.
Homework Assignment #4 due Friday, November 6, 1998
Prob. 4-1. Two small spheres, each with mass 8.5 g, are hung by silk threads of length
0.800 m from the same point. The spheres are given equal amounts of positive charge and
move apart until each thread makes an angle of 18◦ with the vertical. a) Draw a diagram
showing all forces acting on each sphere. b) Find the magnitude of the charge on each sphere
and the tension in the thread.
Prob. 4-2. Exercise 23-8 on p. 725 in the text.
Prob. 4-3. Problem 23-36 on p. 728 in the text. Also, if b = 1.00 cm and α = 2.00 nC/m,
what is the magnitude of the electric field 1.00 m away from the tube?
LCR sg1.tex 22 Oct 1998 9:13 a.m.