Notes

Review
Final Exam: Tuesday, Dec. 16 Time: 4-7 PM
College Avenue - Gym Annex: Aa - Iz
College Avenue - Main Gym:
Ja – Rz
College Avenue - Scott Hall 135 : Sa - Zz
Additional review sessions:
Monday, December 15, 10:00am-6:00pm in ARC 328
Tuesday, December 16, 10:00am-2:00pm in ARC 328
My office hours: Thursday Dec.11 3 – 4 PM or by appointment
Final (cumulative) Exam:
~15 problems on Chapters 21-28
and ~15 problems on Chapters 29-32
1
The required end of semester post survey* is available at
https://secure.rutgers.edu/secureforms/Login.aspx?ID=Physics_Survey. You are
required to take the online survey by Friday December 12th at midnight; it will
take about 15 to 20 minutes to complete.
Final reminder: December 7, 500 PM was the last day and time to request
conflict exam for Final Exam (can request conflict exam if have another exam at
same time OR have 3 exams in 24 hour period). Must e-mail Professor Cizewski
[email protected] with details of why you are requesting conflict
exam.
All of the instructors in Physics 227 would appreciate your completing the online course evaluations for the lectures and its associated recitations. We take
these evaluations seriously as we strive to improve the effectiveness of our
teaching.
*You are required to complete all four parts of the pre and post tests and
surveys, but you have a no-penalty option of having your data withheld from
the study if you choose not to participate. Your responses to these tests and
surveys will have no bearing on your course grade. Your instructors will not see
your scores, and will keep track only whether or not you took the tests. To get
full credit for this required part of the course you must complete all four
components.
Preparation for the Final Exam
(a) Start earlier!
(b) Review the concepts (lectures + textbook) and prepare your equation
sheet. Think how you can use every equation on your sheet, what types of
problems can be solved with these equations.
(c) Work on practice exams.
(d) Review all HW and Iclicker questions.
(e) If you still have time/questions, go over the end-of-chapter problems
(you don’t need to solve them, just check that you know how to approach
them).
At the Exam
(a) Make sure you understand the problem, read the problem formulation
carefully. Make a drawing!!! If you remain uncertain raise your hand and
ask the proctors.
(b) Get the units right. It is easy to eliminate the answers with wrong units.
This applies to formulas too.
3
Maxwell’s Equations
 Gauss’s Law: electric flux begins and ends on charges (or at infinity).
𝑄𝑒𝑒𝑒𝑒
𝜀0
�
𝐸 ∙ 𝑑𝐴⃗ =
�
𝐵 ∙ 𝑑𝐴⃗ = 0
�
𝐸 ∙ 𝑑𝑙⃗ = −
�
𝐵 ∙ 𝑑𝑙⃗ = 𝜇0 �
𝑠𝑠𝑠𝑠
 No magnetic monopoles; magnetic field lines don’t begin or end.
𝑠𝑠𝑠𝑠
 Faraday’s Law of electromagnetic induction; a time-dependent ΦB generates E.
𝑙𝑜𝑜𝑜
𝑑
� 𝐵 ∙ 𝑑𝐴⃗
𝑑𝑑 𝑠𝑢𝑢𝑢
 Generalized Ampere’s Law; B is produced by both currents and time-dependent ΦE.
𝑙𝑜𝑜𝑜
𝑠𝑢𝑢𝑢
 The force on charge.
𝐹⃗ = 𝑞 𝐸 + 𝑣⃗ × 𝐵
𝐽⃗ + 𝜖0
𝜕𝐸
∙ 𝑑𝐴⃗
𝜕𝜕
6
R-L-C circuits
𝑃𝑎𝑎 = 𝑉𝑟𝑟𝑟 ∙ 𝐼𝑟𝑟𝑟 cos 𝜙 =
cos 𝜙 =
1
𝑉 ∙ 𝐼 cos 𝜙
2 0 0
2𝑃𝑎𝑎
30𝑊
=
= 0.6
𝑉0 ∙ 𝐼0 100𝑉 ∙ 0.5𝐴
arccos 0.6 ≈ 0.93
7
R-L-C circuits (cont’d)
An L-R-C series circuit with an inductance of 0.119H , a
resistance of 244 Ω, and a capacitance of 7.27 µF carries
an rms current of 0.446A with a frequency of 391Hz .
𝜔 = 2455 𝑟𝑟𝑟/𝑠
Whatisisthe
thephase
phaseangle?
angle?
1.1.What
𝑉0 𝑒
𝑖 𝜔𝜔+𝜙
= 𝐼0 𝑒
𝑖𝑖𝑖
𝑍0 𝑒
𝑖𝑖
𝐼0 = 𝑉0 𝑒 𝑖𝑖
𝑉0 𝑒 𝑖𝑖 = 𝐼0 𝑍0 𝑒 𝑖𝑖
𝑍 = 𝑅 + 𝑖𝑋𝐿 − 𝑖𝑋𝑐 = 𝑅 + 𝑖 𝜔𝜔 −
1
𝜔𝜔
1
𝜔𝐿 −
2455 ∙ 0.119 − 2455 ∙ 7.27 ∙ 10−6
𝜔𝐶
tan 𝜙 =
=
𝑅
244
2. What is the power factor for this circuit?
3.What
Whatisisthe
theimpedance
impedanceof
ofthe
thecircuit?
circuit?
3.
4. What is the rms voltage of the source?
−1
≈ 0.97
1 −𝑖𝑖
𝑒
𝑍0
arctan 0.97 ≈ 0.77 𝑟𝑟𝑟
cos 0.77 = 0.72
𝑍0 =
𝐼𝐼
1
𝑅 2 + 𝜔𝜔 −
𝜔𝜔
2
𝜙
𝜙
𝑉
𝐼
1/𝑍
𝑅𝑅
= 339Ω
𝑉𝑟𝑟𝑟 = 𝐼𝑟𝑟𝑟 ∙ 𝑍0 = 151𝑉
5. What average power is delivered by the source?
6. What is the average rate at which electrical energy
is converted to thermal energy in the resistor?
𝑃𝑎𝑎 = 𝑉𝑟𝑟𝑟 ∙ 𝐼𝑟𝑟𝑟 cos 𝜙
= 151 ∙ 0.446 ∙ 0.72 = 48.6𝑊
8
Calculation of Mutual Inductance (cont’d)
Consider two loops, radii a (very small) and b, distance z apart. Find the mutual
inductance.
Φ1→2 Φ2→1
We have two options:
𝑀=
=
𝐼
𝐼2
𝑎
1
loop 2
However, if the current is flowing in loop 1, the magnetic
field at the location of loop 2 is almost uniform, and this
𝑧
simplifies our calculations a great deal:
𝑏
𝜇0 𝐼1
𝑏2
𝐵1 =
loop 1
2 𝑏2 + 𝑧 2 3/2
The flux of B1 through loop 2:
Φ1→2 =
and the mutual inductance
𝜋𝑎2 𝐵1
𝜇0 𝐼1
𝜋𝑎 2 𝑏2
=
2 𝑏2 + 𝑧 2 3/2
Φ1→2 𝜇0
𝜋𝑎 2 𝑏2
𝑀=
=
𝐼1
2 𝑏2 + 𝑧 2 3/2
9
Originally a capacitor with capacitance C is fully
charged to Q0. The capacitor is now connected to a
resistor R and DISCHARGES. At what time t is the
energy stored in the capacitor 1/5 the maximum
energy? (i.e., when is U(t) = Umax/5)?
a) t = RC
b) t = RC/5
c) t = [RCln(5)]/2
d) t = RCln(5)
e) t = 2RCln(5)
A wire of length L is in a region of uniform magnetic field ⃗B. Which of
the following statements about the force ⃗F is TRUE?
I. If the current in the wire flows straight down and the magnetic field
points due west, the force on the wire points due north.
II. If the current in the wire flows due east and the magnetic field points
straight down, the force on the wire points due north.
III. If the current in the wire flows due west and slightly up and the
magnetic field points due east, the force on the wire points due north.
a) I and II and III are TRUE.
b) Only I is TRUE and II and III are false.
c) Only II is TRUE and I and III are false.
d) Only I and II are TRUE and III is false.
e) Only III is TRUE and I and II are false.
A metal rail with a sliding rod is in a uniform,
constant magnetic field B directed out of the plane
of the board. The rod is sliding at speed v to the
right. If the resistance of the assembly is R, what
will be the induced current?
a) Zero
b) Bav/R clockwise
c) Bav/R counterclockwise
d) Bbv/R clockwise
e) Bbv/R counterclockwise
A metal ring with diameter d =4 cm is placed between the
north and south poles of large magnets with the plane of
its area perpendicular to the magnetic field. These
magnets produce an initial uniform field of B =1 T
between them. The magnets are gradually pulled apart,
causing this field to remain uniform but decrease steadily
at 0.25 T/s. What are
(a) The magnitude of the electric field E induced in the
ring and (b) in which direction does the current flow as
viewed by someone on the south pole of
the magnet?

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