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Recitation Instructor: ______________________ Recitation Section Letter: _____
PHYSICS 2135 COURSE HANDBOOK
Spring 2015
Textbook: Physics, Custom Edition of Young and Freedman, 13th Edition.
This handbook is your guideline for Physics 2135: Engineering Physics II procedures. If corrections
are required, the “official” version of this handout is maintained on the Physics 2135 web site.
Major Course Elements
Lecture (Mondays and Wednesdays). Lectures will elaborate on concepts that are difficult to
master or understand on a first reading of the material. In addition, examples will be worked to
demonstrate the concepts and assist in the development of your problem solving skills. You are
expected to have completed your reading assignment prior to lecture.
Recitation (Tuesdays and Thursdays). Recitation will be an additional source of instruction on
important course concepts, with emphasis on developing the problem solving skills necessary for
completion of the assigned homework. Your mastery of the material and your problem solving
skills will be tested through collection of the assigned homework and student presentation of
homework at the chalkboard.
Physics Learning Center (Mondays and Wednesdays). This is an open learning environment
where you can solve problems in informal student groups, get help and insight in a relaxed
setting, and prepare for your recitation class. You can come at any time during operating hours in
rooms 129-130 of the Physics Building. At least one physics instructor will be there to help you.
Laboratory (every other week beginning the second week of classes). See the “Physics 2135
Laboratory” handout for details. This handout is available from your laboratory instructor, or
online at http://campus.mst.edu/physics/courses/2135lab/. The laboratory is designed to reinforce
concepts learned in lecture and recitation, to connect those concepts to physical experience, to
illustrate scientific methods, and teach measurement theory.
Sources of Points and Grading
Exams. There will be three hour exams, given only at 5:00 PM on the Tuesdays listed in the
Schedule of Classes. See the course website for location where the exams will be given for your
recitation section. The final exam is at 7:30 AM, Friday, May 15. These four exams are worth
200 points each. Your lowest exam score (out of the three exams and the final) will be dropped.
End-Material Test. A 50-point end-material test will be given concurrent with the final exam on
May 15. This test will cover material presented in class after the material for Exam 3.
Lecture Quizzes. Twelve multiple choice quizzes will be given to test your comprehension of
the fundamental ideas in recent assignments. The two lowest quiz scores will be dropped.
1
Recitation Homework. On unannounced recitation days, assigned homework will be collected,
or you may be asked to work and hand in a homework problem (or one similar to it) during
recitation. A total of six homework sets will be collected and your lowest score will be dropped.
Recitation Boardwork. Your recitation instructor will call students to solve a homework problem
(or one similar to it), usually on the blackboard, and without the use of notes. If you are absent, a
grade of zero will be recorded. One lowest boardwork score will be dropped.
Laboratory. There will be six laboratories during the semester. Your reports are to be turned in
to your lab instructor at the end of the lab period. Lab reports will be graded on the basis of 100
points, and reports will be returned by your lab instructor. The lowest lab report score will be
dropped. Each Physics 2135 student must purchase a lab manual. Manuals are available in the
department office. Students not purchasing a lab manual will receive a laboratory grade of 0.
Course Points:
Exams:
End Material Test:
Lecture Quizzes:
Recitation Homework:
Boardwork:
Six Laboratories:
Total
600
50
50
50
100
150
1000
One exam, two quizzes, and one homework score will be dropped. Your boardwork points will
be your average boardwork percentage after the lowest boardwork score is been dropped. Your
lab points will be 1.5 times your average lab percentage after the lowest lab grade is dropped.
Grading is on an absolute scale. The cut-offs for grades are:
A (≥ 89.50%)
B (≥ 79.50%)
C (≥ 69.50%)
D (≥ 59.50%)
F (< 59.50%)
≥
≥
≥
≥
<
895.0
795.0
695.0
595.0
595.0
Some Course Rules
Those participating in a major university or intercollegiate event on the day of an exam
may take the exam on that day at some time other than the normal time if they submit a
written request for an excused absence and if the event’s Faculty Sponsor can ensure exam
security. The student must submit a written request (email is acceptable) to Dr. Pringle,
acknowledged in writing (email is acceptable) by the event's Missouri S&T Faculty Sponsor, no
later than the end of the last Wednesday lecture the week before the exam. The Faculty Sponsor
must be willing to arrange proctoring and ensure exam security. More information is available at
http://campus.mst.edu/physics/courses/24/CourseInformation/sponsor_mst.pdf.
Your lowest exam score will be dropped. This accommodates students who miss one test due
to reasons beyond their control (minor illness, athletic events, family events, etc.).
2
There are NO make-ups of exams, lecture quizzes, recitation assignments, labs, or the endmaterial test. Any missed assignment will result in a grade of zero. The two lowest lecture quiz
scores, and the single lowest homework, boardwork, lab, and exam score will be dropped. There
will be no laboratory make-ups. Laboratory policies are set by faculty in charge of the labs.
Because the lowest lab score is dropped, no make-ups will be given.
Regrade policy. Requests for regrades must be submitted no later than the end of the
second recitation meeting after the general return of the assignment, except that lab
regrade requests must be submitted the day the lab report was returned to you. All regrade
requests must be submitted to your recitation instructor. Laboratory report regrade requests are
not to be submitted to your laboratory instructor. You must compose a detailed but brief written
statement on a separate sheet of paper explaining why you are requesting a regrade. Attach the
sheet to the front of the full assignment and submit it to your recitation instructor by the
appropriate deadline.
There are occasional instances in which a score is not entered correctly in the spreadsheet
record. In such an event, you must bring your recitation instructor the assignment that was
incorrectly recorded, and the correction will be made. It may be necessary to bring all
assignments of that type (homework, quizzes, etc.) in order to have your scores correctly entered.
Spreadsheet corrections involving exams must be requested within two weeks of posting of the
exam grades. Other spreadsheet corrections must be requested before the start of the Final Exam.
Academic dishonesty will be dealt with severely (see http://registrar.mst.edu/academicregs).
Disruptive talking and other distractions will not be tolerated. There are too many students
in a room to allow disruptive behavior. A course instructor may request the campus Judicial Officer
to take effective disciplinary action after issuing a single warning (see Student Code of Conduct at
http://registrar.mst.edu/academicregs).
Students with inadequate attendance may be dropped. Any student who has inadequate
attendance, as evidenced by 7 confirmed absences or by missing a total of 7 graded assignments
of any kind (exams, homework, quizzes, boardwork, and labs) may be flagged with an
S&TConnect Early Alert. Students who fail to take the recommended action are subject to being
dropped if a subsequent class or assignment is missed.
Appeals. In rare cases, you may believe an exception to a course rule should be made. In this
case, you may file a written appeal with your recitation instructor. Appeals must be filed within
one week of the occurrence of the circumstance that causes your appeal, or by the end of your
last recitation of the semester, whichever comes first. Your appeal will be carefully considered
by the entire Physics 2135 teaching staff. This appeals policy applies to course rules given in this
handbook, but does not apply to laboratories. Minor illness, lack of preparation, “I did poorly on
two exams,” non-emergency family events, oversleeping, “I forgot about it,” etc., are not reasons
for filing an appeal.
Other Course Policies. See http://campus.mst.edu/physics/courses/24/CourseInformation/ for
other course policies not described in this handbook.
3
Complaints About the Course
Unresolved complaints about a laboratory or recitation instructor: Occasionally, a student
has a conflict with a laboratory or recitation instructor. It is hoped that any complaints can be
resolved in a collegial manner through discussions between student and instructor. However, if
such a situation continues or remains unresolved, please feel free to discuss it with Dr. Pringle.
He will act as a go-between, or you may be able to switch to a different section. If your
difficulties are with your laboratory instructor, you may also contact Dr. Hagen who is in charge
of the laboratory portion of the course, or Dr. Waddill who is assisting with the labs.
Unresolved complaints about the course: It is hoped that any complaints about the course can
be resolved in a collegial manner through discussions with Dr. Pringle. However, if there are any
complaints that cannot be resolved, you may take them up with Dr. Dan Waddill, Chairman,
Physics Department ([email protected]).
Course Assistance
If you require additional assistance you should not hesitate to take advantage of the multiple
opportunities available to receive help. You may arrange for extra assistance with your recitation
instructor or through the Physics Learning Center (PLC). The PLC for Physics 2135 will operate
on Mondays and Wednesdays between 2:00-4:30 pm and 6:00-8:30 pm. If you desire additional
or alternate learning assistance and consultation for this course visit the web site of the Learning
Enhancement Across Disciplines (LEAD) program at http://lead.mst.edu/.
If you have a documented disability, you are encouraged to meet with Dr. Pringle to discuss the
accommodations you will need. You should request that the Disability Services staff
(http://dss.mst.edu/) send a letter to Dr. Pringle verifying your disability and specifying the
accommodation you will need. We are not allowed to discuss your grades or academic
performance with parents, guardians, etc., unless you fill out this form:
http://registrar.mst.edu/media/administrative/registrar/documents/parentswaiverform.pdf.
Accessing Physics 2135 Course Material on the Web
Course handouts, schedules, assignments, your grades, and other course information may be
found on the Physics Department Web Site http://physics.mst.edu/classes/class24/.
Viewing Grade Spreadsheet in Microsoft Excel
In Column D (Student Personal Identification Number), find the PIN that was assigned to you.
The row with that number gives all the scores that your instructor has recorded for you prior to
the last update of the course spreadsheet. Verify that your scores entered for the reported
assignments are correct. If they are not, bring the assignments in question to your recitation
instructor so that your scores can be correctly entered. It may be necessary to bring all
assignments of that type (homework, quizzes, etc.) in order to have your scores correctly entered.
This spreadsheet is usually updated weekly after the first exam.
Course handout last revised: 11:03 am, January 13, 2015.
4
Physics 2135 Syllabus
Spring 2015
Prof. Allan Pringle
Office: 122 Physics Phone: 341-4031 email: [email protected]
Course Web Site: http://physics.mst.edu/classes/class_24.html
Textbook: Physics, Custom Edition of Young and Freedman, 13th Edition
Physics 24, Spring 2015 Homework Assignments. Last revised: 11:00 am, January 7.
Lecture
Monday, January 19
Martin Luther King Day
Recitation/Exam
1. Tuesday, January 20
Vector review (to be handed out in class)
1. Wednesday, January 21
read 1: 1-4
Electric Charge, Coulomb’s
Law, Electric Field
2. Monday, January 26
read 1: 5
Electric Field of a Charge
Distribution
2. Thursday, January 22
1: 13, 18 (also express the force in unit vector
notation), 28, 87, Special Homework #1
3. Wednesday, January 28
read 1: 6-7; 22: 1-4
Electric Field Lines, Electric
Dipoles, Electric Flux, Gauss’
Law
4. Monday, February 2
read 2: 4-5
Gauss’ Law Calculations,
Conductors and Electric Fields
4. Thursday, January 29
1: 57, 62; 2: 12 (use Gauss’ Law), 34, Special
Homework #2 (reminder: all solutions must begin
with starting equations)
5. Wednesday, February 4
read 3: 1-2
Electric Potential, Electric
Potential Energy
6. Monday, February 9
read 3: 3-5
Potential of Charge
Distribution, Equipotentials,
Potential Gradient
6. Thursday, February 5
3: 4, 10, 14, 21, 61
7. Wednesday, February 11
read 4: 1-2
Capacitance, Capacitors in
Series and Parallel
8. Monday, February 16
Exam 1 Review
8. Thursday, February 12
4: 5, 6, 11, 57, 64 (reminder: all solutions must
begin with starting equations)
9. Wednesday, February 18
read 4: 3-4
Energy Stored in Capacitors
and Electric Fields, Dielectrics
10. Thursday, February 19
4: 24, 35, 44, Special Homework #5
3. Tuesday, January 27
1: 53, 90, 91a, 98 (also express the force in unit
vector notation), 100 (reminder: all solutions must
begin with starting equations)
5. Tuesday, February 3
2: 19 (you only need to derive the expression for
the electric field once), 23, 40, 47, Special
Homework #3 (reminder: all solutions must begin
with starting equations)
7. Tuesday, February 10
3: 29, 31, 39, 86abc, Special Homework #4
(reminder: all solutions must begin with starting
equations)
9. Tuesday, February 17
Test Preparation Homework #1
Exam 1: 5:00 pm, chapters 1.1-4.2
Lab
No Labs
Odd
O1: Coulomb’s
Law
Even
E1: Electrical
Instruments
Odd
O2: Fields and
Potentials
Even
E2: Capacitors
1
Physics 2135, Spring 2015, Homework Assignments, page 2.
Lecture
10. Monday, February 23
read 5: 1-3
Electric Current, Current
Density, Resistance
Recitation/Exam
11. Tuesday, February 24
5: 4, 22, 25, 56, 58
11. Wednesday, February 25
read 5: 4-5
EMF, Electric Power
12. Monday, March 2
read 26: 1-2
(last drop day)
Resistors in Series and
Parallel, Kirchoff’s Rules
12. Thursday, February 26
5: 32, 39, 46, 70, 72
13. Wednesday, March 4
read 6: 3-4
Electrical Instruments, RC
Circuits
14. Monday, March 9
read 7: 1-2, 4-6
Magnetic Field, Motion of
Charged Particle in Magnetic
Field, Magnetic Forces on
Currents
14. Thursday, March 5
6: 38, 51, 83, 84, Special Homework #6 (reminder:
all solutions must begin with starting equations)
15. Wednesday, March 11
read 7: 3, 7
Magnetic Flux, Gauss’ Law
for Magnetism, Magnetic
Torque
16. Monday, March 16
Exam 2 Review
17. Wednesday, March 18
read 8: 1-4
Magnetic Field of Current,
Biot-Savart Law, Field of
Wires, Force between
Conductors
13. Tuesday, March 3
6: 6, 13, 22, 59, 65
15. Tuesday, March 10
7: 7, 31, 39 (you may express your answer using
unit vector notation), 61, 74
Lab
Odd
O3: ResistanceMaterials,
Geometry
Even
E3: Ohm’s
Law, Internal
Resistance
No Labs
Thursday, March 12
Spring Recess: no recitation; no homework
16. Tuesday, March 17
Test Preparation Homework #2
Exam 2: 5:00 pm, chapters 4.3-7.7
Odd
O4: Series RC
Circuits
17. Thursday, March 19
8: 8, 16, 67, 74 (reminder: all solutions must begin
with starting equations)
2
Physics 2135, Spring 2015, Homework Assignments, page 3.
Lecture
Monday, March 23
Spring Break
Recitation/Exam
Tuesday, March 24
Spring Break
Wednesday, March 25
Spring Break
18. Monday, March 30
read 8: 5-7
Magnetic Field of Current
Loop, Ampere’s Law,
Solenoids
Thursday, March 26
Spring Break
18. Tuesday, March 31
Even
8: 35, 42, 46, 49, Special Homework #7 (reminder: E4: Current
all solutions must begin with starting equations)
Balance
19. Wednesday, April 1
read 9: 1-4
Induction, Faraday’s Law,
Generators, Lenz’s Law,
Motional emf
19. Thursday, April 2
9: 24, 25, 27, 56, Special Homework #8 (reminder:
all solutions must begin with starting equations)
20. Monday, April 6
read 9: 5-7
Induced Electric Field, Eddy
Currents, Displacement
Current
20. Tuesday, April 7
9: 13, 37, 41, 53 (why does the case a→0 differ
from the result for a conducting bar?), 65 (three
problems are a review of material from the
previous lecture)
21. Wednesday, April 8
read 10: 1-4
Electromagnetic Waves
21. Thursday, April 9
10: 13, 20 (in part b, do not calculate the rms value
of the electric field; instead, calculate the
amplitudes of the electric and magnetic fields in
the beam), 22, 23, 54
22. Tuesday, April 14
11: 1, 10, 48, 51, Special Homework #9
22. Monday, April 13
read 11: 1-4
Light: Reflection, Refraction,
Dispersion
23. Wednesday, April 15
read 12: 1-2
Concave and Convex Mirrors
Lab
No Labs
Odd
O5: Generator
Even
E5: Snell’s Law
23. Thursday, April 16
12: 6, 10 (the outside bottom of the bowl is facing
you; draw a ray diagram), 68, 69, 72 (draw a ray
diagram)
24. Monday, April 20
Exam 3 Review
Last withdraw day is Friday, April 17.
24. Tuesday, April 21
Test Preparation Homework #3
Exam 3: 5:00 pm, chapters 8, 9, 10
25. Wednesday, April 22
read 12: 3-8
Lenses, Optical Instruments
25. Thursday, April 23
12: 26, 29 (draw a ray diagram), 30, 86 (hint: R=∞
for a flat surface), Special Homework #10
Odd
O6: Lenses
3
Physics 2135, Spring 2015, Homework Assignments, page 4.
Lecture
26. Monday, April 27
read 13: 1-3
Double Slit Interference
Recitation/Exam
26. Tuesday, April 28
13: 14, 17, 18, 24, 43
27. Wednesday, April 29
read 13: 4
Thin Film Interference
28. Monday, May 4
read 14: 1-5
Diffraction
27. Thursday, April 30
13: 26, 27, 31, 33, 54
29. Wednesday, May 6
Final Exam Review
29. Thursday, May 7
Final Exam Preparation Homework
Friday, May 15
28. Tuesday, May 5
14: 4, 15, 38, 55, 65
Lab
Even
E6: Dispersion
No Labs
No makeup
labs will be
given!
No Labs
End-Material Test and Comprehensive
Final Exam, 7:30-9:30 AM
4
Starting Equations for Physics 2135
Frequently-Used Official Starting Equations From Engineering Physics I:
1
2
x= x 0 + v 0x ∆t + a x ( ∆t )
2
E f − Ei =
( Wother )i→f
Wnet = ∆K
E= K + U
 
PF= F ⋅ v
vx 2 =
v 0x 2 + 2a x ( x − x 0 )
v x = v 0x + a x ∆t
1
mv 2
2
ar =
v2
r
PF =
( Wexternal )i→f

dWF
dt


p = mv
∆U =U f − U i =
− ( Wconservative )i→f
E = Paverage t
 

=
Pi P=
0
f if ∑ Fext
K=

∑ F = ma
=
− ( Wconservative )i→f if ∆K=0
Constants
1
N ⋅ m2
= 9 ×109
k=
4πε0
C2
8.85 ×10−12
ε=
0
e 1.6 ×10−19 C
=
= 1.6 ×10−19 J
1 eV
m electron
= 9.11×10−31 kg
m proton
= 1.67 ×10−27 kg
C2
N ⋅ m2
m 0 = 4π×10−7
c= 3 ×108
T⋅m
A
g = 9.8
m
s2
E sheet =
s
2e 0
m
s
Electric Force, Field, Potential, and Potential Energy
F=k


F = qE
q1q 2
r122
d
d
p = qd, from - to +
  
τ = p×E
U dipole
d
f d
U f − Ui =
−q ∫ E ⋅ d 
∆U =q∆V =q ( Vf − Vi )
V(r) =
q
r2
d d
=−p ⋅ E
E=k
i
1 q
4πε 0 r
U=
1 q1q 2
4πε 0 r12

q
E = k 2 rˆ
r
d d
Φ E = ∫ E ⋅ dA
d d q enclosed
E
∫ ⋅ dA =e0
d
f d
Vf − Vi =
−∫ E ⋅ d 
∆V =
Ed
i
V=
1
dq
∫
4πε 0 r
Ex = −
∂V
∂x
Circuits
Q
C=
V
κε0 A
C=
= κC0
d
1
1
=∑
Ceq
i Ci
Iav =
R=
ρ
A
P=V
dq
dt
τ =RC
ρ=
∆Q
∆t
I=
1
σ
1
1 Q2 1
2
=
U
CV
= =
QV
2
2 C 2
dQ
dt
J=
I
A
ρ = ρ0 1 + α ( T − T0 ) 
2
=
P IV
=
V
= I2 R
R
∑I = 0
at any circuit junction
Ceq = ∑ Ci
i
d
d
J = nqv d
R eq = ∑ R i
i
Q=
( t ) Qfinal [1 − exp(− t / t)]
∑V = 0
V = IR


J = σE
1
1
=∑
R eq
i Ri
Q=
( t ) Q0 exp(− t / t)
around any closed circuit loop
Gray shading around equation means I
don’t recommend that you use it unless
you REALLY know what you are doing.
Magnetic Force, Magnetic Fields, Inductance

  

 

 
F= q E + v × B
F
= IL × B
=
F qv × B
(
 
U = −µ ⋅ B
B=
dΦ B
d
Idispl = κε0
ΦB=
  
τ = µ×B
d d
B
∫ ⋅ dA
d d
B
0
∫ ⋅ dA =
d µ 0 I dsd × rˆ
dB =
4π r 2
 µ 0 qv × rˆ
B=
4π r 2
µ NI
B= 0
2πr
−
∫ E ⋅ ds =
dt


µ =NIA (N=1 for single loop)
d d
dΦ 

B
∫ ⋅ ds = µ0  Iencl + κe0 dt E 
µ0 I
2πr
N
B=
µ0
I=
µ0 n I

d
)
ε = −N
dΦ B
dt
dΦ E
dt
Electromagnetic Waves

=
S
I=
1  
E×B
µ0
1
1 E 2max 1 cB2max
2
=
I =S = c ε 0 E max =
2
2 m0c 2 m0
P
area
1
1 B2
u B =u E = ε0 E 2 =
2
2 µ0
uB =
k=
1 B2max
4 m0
1
ε 0 E 2max
4
2π
ω = 2πf =
T
2π
λ
1
ε 0m 0
1
1 B2
2
u =ε 0 E max
= max
2
2 m0
=
I
uE =
E max E
=
= c=
Bmax B
=
S c u
fλ=
ω
= c
k
Pr ad =
T=
I
2I
or
c
c
1
f
Optics
v = fλ =
ω
k
=
I I max cos 2 φ
θi =θr
1 1 1
+ =
s s' f
 1
1
1 
=
( n − 1)  − 
f
 R1 R 2 
φ
I = I0 cos  
2
2
n=
f=
λ
λn =
n
c
v
R
2
m
=
λ d sin θ
m=
y'
s'
= −
y
s
n a sin=
θa n b sin θb
na nb nb − na
+
=
s
s'
R
m=
2π
1

φ
d sin θ
m+ =
 λ d sin θ =
λ
2

2π
β
a sin θ
a sin θ= mλ =
λ
 sin ( β / 2 ) 
I = I0 

 (β / 2 ) 
2
=
R
n s'
y'
= − a
y
n bs
I0 = 4 I
λ avg
= Nm
∆λ
Mathematics
Vsphere=
4 3
pr
3
A sphere = 4p r 2
A cylinder = 2π r L
(excluding ends)
Last modified: 3:56 pm, October 17, 2014.
Physics 2135
Special Homework Assignment #1
1. A point charge +Q is located at the origin, and a point charge -Q
is located at (x,y) = (0,L).
y
-Q
(a) Find the electric field at point P, which is a distance L away from
both +Q and -Q, as shown in the diagram. Express your answer in
unit vector notation using the coordinate system given.
L
L
P
L
+Q
(b) A point charge -2Q is placed at point P. Find the Coulomb force on the charge
-2Q due to the other two charges. Express your answer in unit vector notation using the
coordinate system given.
x
Physics 2135
Special Homework Assignment #2
In each box shown below, draw electric field lines in the region around the objects. Assume the
boxes are far from each other.
Positive point charge
Two insulating spheres coated with positive surface charge
Physics 2135
Special Homework Assignment #3
An infinitely long insulating cylindrical shell has an inner radius a, an outer radius b, and an
unknown uniform positive charge density ρ (charge per unit volume) distributed in the region
between r = a and r = b.
(a) Using Gauss’s law, find the electric field in the hollow inner region r < a. Begin with a
statement of Gauss’s Law and justify all steps leading to your answer.
a
b
(b) Suppose the electric field at the outer edge of the cylindrical shell (i.e., at r = b) is measured,
and is found to have a magnitude of E0. Use Gauss’s law to express the charge density ρ in terms
of the quantities E0, a, b, and any fundamental constants you may need. Leave your answer in
symbolic form.
(c) Find the magnitude E of the electric field at a radial distance a < r < b from the center of the
cylindrical shell. Express your answer in terms of fundamental constants and some combination
of a, b, r, E0, and/or ρ.
Physics 2135
An insulating rod of
length L has a total
charge of +Q uniformly
spread along its length.
The rod lies along the xaxis with its left end
located at x = a.
Special Homework Assignment #4
y
+Q
x
a
L
(a) Find the electric potential at the origin.
(b) A charge of –q is now moved from infinity to the origin. How much work was done by the
external agent which moved the charge –q?
(c) What is the direction of the electric force on the charge –q when it is at the origin?
Physics 2135
An isolated capacitor of unknown
capacitance C has been charged to a
potential difference of 100 V. When the
charged capacitor is then connected in
parallel to an initially uncharged 10 µF
capacitor (µ stands for 10-6), the voltage
across the combination is 30 V.
Special Homework Assignment #5
Vab=100
a
Vcd=30
b
C?
c
d
C?
C1=10µF
before
after
(a) Calculate the unknown capacitance.
(b) Calculate the energy Uinitial stored in the isolated capacitor when it was charged to 100 V, and
the total energy Ufinal stored in the parallel combination of the two capacitors.
Physics 2135
Special Homework Assignment #6
For the circuit shown R = 15 kΩ, C = 6 μF, and ΔV = 30 V. Initially the capacitor is uncharged.
The switch S is then closed and the capacitor begins to charge. After the switch is closed, how
much time will elapse before the current through the resistor is one-third of its maximum value?
What is the charge on the capacitor at this time?
C
R
S
ΔV
Physics 2135
Special Homework Assignment #7
A very long wire carrying a current I has a perfectly
circular loop of radius R in it (the wire is continuous
and is insulated so there is no contact where the wire
crosses over itself). Determine the magnitude and
direction of the magnetic field B at the center of the
circular loop (point P). Your analysis must begin
with starting equations. Express your answer using
unit vector notation.
I
P
y
R
I
x
I
Physics 2135
Special Homework Assignment #8
Consider a 1.5 V battery with a 0.3 Ω resistor attached to two
conducting, frictionless rails 0.200 m apart. The entire
apparatus is in a uniform magnetic field B directed out of the
page and of magnitude 0.400 T perpendicular to the rails. A
conducting bar can slide over the rails perpendicular to them
as well as to the field. All other resistances in the problem are
negligible compared to the 0.3 Ω resistor. The bar is placed on
the rails, starts from rest, and is observed to accelerate.
1.5 V
B
0.3 Ω
(a) What is the direction of the bar’s acceleration?
x
(b) What is the direction of the emf induced in the bar?
(c) Use Faraday’s Law to calculate the magnitude of the induced emf when the bar reaches a
speed of 12.0 m/s.
(d) Calculate the current in the bar when its speed is 12.0 m/s.
0.2 m
Physics 2135
Special Homework Assignment #9
An optical fiber consists of a glass core with index of refraction ng = 1.52 surrounded by a
coating with index of refraction nc = 1.25. The fiber is submerged in water
(nw = 1.33) and light enters the end of the cable from the water at an angle θ as shown. The light
strikes the surface between the glass and the coating at the critical angle θc so that the light is
refracted along the boundary between the glass and the coating. Determine the angle θ.
coating
nc=1.25
water
nw=1.33
θ
θc
glass
ng=1.52
Physics 2135
Special Homework Assignment #10
A lens forms an image of an object. The object is 20.0 cm from the lens. The image is formed
15.0 cm from the lens on the same side as the object.
(a) What is the focal length of the lens? Based on the results of your calculation, is it a
converging or diverging lens?
(b) If the object is 8.0 mm tall, how tall is the image? Based on the results of your calculation, is
it upright or inverted?
(c) Verify your calculations by making a complete a ray diagram showing the formation of the
image using the figure provided. Adjacent marks on the principal axis are separated by 10.0 cm.
O
Lens