College of Arts and Sciences
Department of Mathematics, Statistics, and Physics
Physics Program
Instructors: Dr. D. Al‐Abdulmalik and Dr. H. Merabet
100
Name………………………….…………..……………………..….…………………………….
Student ID…………………………………………….List #…….……………………………
Section:…………………….………………………………………….………………………….
Physics for Engineers II
PHYS 193 (all sections), Fall 2013
Final Exam
January 7, 2014
Please read the following instructions carefully before you start answering:
1. Make sure that you have 12 pages including two parts, A and B. Part A consists of 10 multiple choice questions, while Part
B consists of 4 short problems.
2. Answer all the questions and show all the steps of your work in a clear tidy way.
3. Calculators are permitted but no electronic dictionaries.
4. Include units in all calculations and answers.
5. All your work must be done on your exam paper; no loose papers are allowed. If additional space is required use the last
page and indicate that this has been done.
6. This is a timed exam (120 min). Do not spend too much time in any particular question.
Best Wishes
1
Part A: Please choose the correct answer for each question and justify your choice in the space provided.
Question 1: (6 pts) A +20 nC point charge is placed on the x-axis at x = 2.0 m, and a –25 nC point charge is placed
on the y-axis at y = –3.0 m. What is the direction of the electric field at the origin?
A) 209o
B) 61o
C) 29o
D) 241o
E) 151o
Justification:
Question 2: (6 pts) The electric field in a region of space is given by Ex = (3.0x) N/C, Ey = Ez = 0, where x is in m.
Points A and B are on the x axis at xA = 3.0 m and xB = 5.0 m. Determine the potential difference VB–VA.
A) -24 V
B) +24 V
C) -18 V
Justification:
2
D) +30 V
E) -6.0 V
Question 3: (6 pts)
p If VA–VB = 50 V, how
w much enerrgy is storedd in the 36-µF
F (C2) capaccitor? Let C1 = 72-µF and
d
C3 = 54-µF.
A) 50 mJ
B) 28 mJJ
C) 13 mJJ
D) 8.9 mJ
m
E) 17 mJJ
Justtification:
Question 4: (6 pts)
p A wire, 0.60
0 m in len
ngth, is carry
ying a currennt of 2.0 A is placed at a ccertain anglee with respecct
to thhe magnetic field
f
of stren
ngth 0.30 T. If the wire experiences
e
a force of 0.18 N, what aangle does thhe wire makee
withh respect to th
he magnetic field?
A) 20o
B) 25o
C) 30o
Justtification:
3
D
D) 35o
E)) 60o
Question 5: (6 pts) The figure below shows three long, parallel current-carrying wires. The magnitudes of the
currents are equal and their directions are indicated in the figure. Which of the arrows drawn near the wire
carrying current 1 correctly indicates the direction of the magnetic force acting on that wire?
A) A
B) B
C) C
D) D
E) The magnetic force is equal to zero
Justification:
Question 6: (6 pts) The figure below shows the time evolution of a uniform magnetic field. Four particular
instants labeled tA to tD are also identified on the graph. The field passes through a circular coil whose normal is
parallel to the direction of the field. At what time does the current induced in the coil have the largest value?
A) tA
B) tB
C) tC
D) tD
E) The current is the same at all these times.
Justification:
4
Question 7: (6 pts) Starting from zero, the electric current takes 2 seconds to reach half its maximum possible
value in an RL circuit with a resistance R, an inductance L and a battery of emf . How long will the current take
to reach 75% its maximum value (measured from the moment when I = 0)?
A) 8 s
B) 4 s
C) 10 s
D) 1 s
Justification:
Question 8: (6 pts) In a given LC resonant circuit,
A) the stored electric field energy is greater than the stored magnetic field energy.
B) the stored electric field energy is less than the stored magnetic field energy.
C) the stored electric field energy is equal to the stored magnetic field energy.
D) all of the given answers are possible.
Justification:
5
E) 2 s
Question 9: (6 pts) What is the phase angle between the voltages of the inductor and capacitor in a LRC series
circuit?
A) zero
B) 45o
C) 90o
D) 180o
E) 270o
Justification:
Question 10: (6 pts) An electromagnetic wave has a magnetic field with rms value of 3.0×10-6 T. What is the
intensity of the wave?
A)
B)
C)
D)
E)
0.1×103 W/m2
3.0×103 W/m2
1.1×103 W/m2
2.1×103 W/m2
1.5×103 W/m2
Justification:
Extra Credit Question: (3 pts) A solenoid of length 5.0 cm has a cross sectional area of 1.0 cm2 and has 300
uniformly spaced turns. The solenoid is wrapped in 180 turns of insulated wire. Calculate the mutual inductance.
6
Part B: Please solve the following problems showing all the steps of your solution.
Problem 1: (10 pts) A line of positive charge is formed into a semicircle of radius R = 50.0 cm as shown in the
figure below. The charge per unit length along the semicircle is described by the expression λ = λ0 cos θ. The total
charge on the semicircle is 18.0 μC.
a) Determine the value of λ0. (3pts)
b) Calculate the total force on a charge of -2.00 μC placed at the center of
curvature. (7pts)
7
Problem 2: (10 pts) An air-filled spherical capacitor is constructed with concentric spherical conducting shells;
inner and other shells of radii ri = 7.00 cm and ro = 14.0 cm, respectively.
(a) Use Gauss’s law to determine the electric field at a point r between the two shells (ri < r < ro). Assume
that the charge on the inner shell is +Q and on the outer shell is –Q. (3pts)
(b) Determine an expression for the potential difference, Vro-Vri, between the two spherical shells. (3pts)
(c) Calculate the capacitance of this capacitor. (4pts)
8
Problem 3: (8 pts) Two long, parallel conductors, separated by 10.0 cm, carry currents in the same direction. The
first wire carries current I1 = 5.00 A, and the second carries I2 = 8.00 A.
(a) What are the magnitude and direction of the magnetic field created by I1 at the location of I2 and by I2
at the location of I1? (4pts)
(b) What is the force per unit length (magnitude and direction) exerted by I1 on I 2 and by I2 on I1? (4pts)
9
Problem 4: (12 pts) In SI units, the electric field in an electromagnetic wave is described by
E y  100 sin 1.00  10 7 x  ωt  . Find:
(a) The amplitude of the corresponding magnetic field oscillations. (4 pts)
(b) The wavelength λ of the wave. (4 pts)
(c) The frequency f of the wave. (4 pts)
End of Exam
10
11
Useful Information
Formulae
,
p
,
,
,

,
,
∆
,
,
∆
,
B ,
B
,
F
B ,
,
,
E

∮ .

,
⁄
21
,
⁄
1
v

,

⁄

,


,
B ,
μ
A
√
,
,
U
,
,
2
√
,
,
cos∅
,
⁄
,
̂
,
cos
,
,
tan∅
,
μ
0 ,
∮ .
,
,
τ
,
∮ .
,
⁄
cos
,
B ,
,
,
,
1
,
,
,
,
cos
,
…
F
,
⋯
,
v
,
B. A
.
,
,
∮ B.

̅
,
⋯,
F
∆
,
,
,
,
∮ .
,
,
⋯ ,
,
.
,
⁄
̅
Constants
k = 9.0  109 N.m2/C2 ,
0 = 8.85  10-12 C2/N.m2 ,
c = 3.00  108 m/s ,
e = 1.60  10-19 C ,
me = 9.1  10-31 kg ,
Integrals
sin
,
0 = 4  10-7 T.m/A,
cos
12
g = 9.8 m/s2
mp = 1.67  10-27 kg
College of Arts and Sciences
Department of Mathematics, Statistics, and Physics
Physics Program
Instructors: Dr. A. Shalaby and Dr. H. Merabet
100
Name………………………….…………..……………………..….…………………………….
Student ID…………………………………………….List #…….……………………………
Section:…………………….………………………………………….………………………….
Physics for Engineers II
PHYS 193 (all sections), Spring 2014
Final Exam
June 15, 2014
Please read the following instructions carefully before you start answering:
1. Make sure that you have 10 pages including two parts, A and B. Part A consists of 8 multiple choice questions, while Part
B consists of 4 short problems.
2. Answer all the questions and show all the steps of your work in a clear tidy way.
3. Calculators are permitted but no electronic dictionaries.
4. Include units in all calculations and answers.
5. All your work must be done on your exam paper; no loose papers are allowed. If additional space is required use the extra
credit page and indicate that this has been done.
6. This is a timed exam (120 min). Do not spend too much time in any particular question.
Best Wishes
1
Part A: Please choose the correct answer for each question and justify your choice in the space provided.
Question 1: (7 pts) Which of the arrows shown in the figure below represents the correct direction of the electric
field between the two metal plates?
A) A
B) B
C) C
D) D
E) none of the above
Justification:
Question 2: (7 pts) An advantage in evaluating surface integrals related to Gauss's law for symmetric charge
distributions is
A) the electric field is of constant magnitude on certain surfaces.
B) the electric field is a constant on any surface.
C) the flux is outward.
D) the charge is always on the surface.
E) the flux is inward.
Justification:
Question 3: (7 pts) A negative charge is moved from point A to point B along an equipotential surface. W hich
of the following statements is true for this case?
A) Work is required to move the negative charge from point A to point B.
B) Not enough information is given to make a statement about the work involved.
C) No work is required to move the negative charge from point A to point B.
D) Work is both required and performed in moving the negative charge from point A to point B.
E) The negative charge performs work in moving from point A to point B.
Justification:
2
Question 4: (7 pts) A charged particle is moving with speed v perpendicular to a uniform magnetic field. A
second identical charged particle is moving with speed 2v pe rpendicular to the same magnetic field. The
frequency of revolution of the first particle is f. The frequency of revolution of the second particle is
A) f/2.
B) 4f.
C) 2f.
D) f.
E) f/4.
Justification:
Question 5: (7 pts) The figure below shows three long, parallel current-carrying wires. The magnitudes of the
currents are equal and their directions are indicated in the figure. Which of the arrows drawn near the wire
carrying current 1 correctly indicates the direction of the magnetic force acting on that wire?
A) A
B) B
C) C
D) D
E) The magnetic force is equal to zero
Justification:
Question 6: (7 pts) A 200-loop coil of cross sectional area 8.5 cm2 lies in the plane of the paper. Directed out of
the plane of the paper is a magnetic field of 0.06 T . The field out of the paper decreases to 0.02 T in 12
milliseconds. What is the direction of the current induced?
A) Clockwise to counterclockwise
B) Clockwise
C) Counterclockwise
D) Counterclockwise to clockwise
E) None of the above
3
Justification:
Question 7: (7 pts) An inductor has a current I = 0.5A cos[(275
equal to 0.5 V. What is the self-inductance of the inductor?
) t] . The maximum emf across the inductor is
A) 3.64 mH
D) 4.37 mH
B) 2.75 mH
C) 0.73 mH
E) 1.43 mH
Justification:
Question 8: (7 pts) The magnetic field of a plane progressive electromagnetic wave in a vacuum is given by
B z = B o cos(ky - ωt). What is the corresponding expression for the electric field?
A) E x = -cB o sin(ky - ωt)
B) E z = cB o sin(ky - ωt)
C) E x = -cB o cos(ky - ωt)
D) E x = cB o cos(ky - ωt)
E) E x = cB o sin(ky - ωt)
Justification:
4
Extra Credit Question: (3 pts) A ten loop coil of area 0.23 m2 is in a 0.047 T uniform magnetic field oriented
so that the maximum flux goes through the coil. The coil is then rotated so that the flux through it goes to zero in
0.34 s. Find the average emf induced in the coil during the 0.34 s?
5
Part B: Please solve the following problems showing all the steps of your solution.
Problem 1 (12 pts): A charge Q 1 = -5.00 µC is located at x = 0 and y = 7.00 cm. A second charge Q 2 = - 4.00 µC
is located at x =14.0 cm and y = 0. A third charge Q 3 = 2.00 µC is located at the origin.
y
a) What is the electric field at the origin due to other charges? (3pts)
b) What is the force on the charge Q 3 due to other charges? (3pts)
Q1
c) What is the electric potential at the point (14.0 cm, 7.00 cm)? (3pts)
d) What is the electric potential energy due to Q 2 and Q 3 ? (3pts)
(Use scientific notation for all your answers)
Q3
6
Q2
x
Problem 2: (10 pts) Calculate the magnitude of the magnetic field at point P of the figure below in terms of R, I 1 ,
and I 2 . What does your expression give when I 1 = I 2 ?
7
Problem 3: (10 pts) Determine the mutual inductance per unit length between two long solenoids, one inside the
other, whose radii are r1 and r2 ( r2 < r1 ) and whose turns per unit length are n1 and n2 .
8
Problem 4: (12 pts) In a region of free space the electric field at an instant of time is
^
^
^
^
^
^
���⃗
E = (80.0 i + 32.0 j – 64.0 k ) N/C and the magnetic field is ���⃗
B = (0.200 i + 0.080 0 j + 0.290 k ) μT.
(a) Show that the two fields are perpendicular to each other.
(b) Determine the Poynting vector for these fields.
End of Exam
9
Useful Information
Formulae
𝑄1 𝑄2
𝐹=𝑘
𝑟2
𝜏⃗ = p
�⃗ × 𝐸�⃗ ,
𝐴
𝑄
𝑅=
𝜌𝑙
𝐴
,
𝑄
𝑉=𝑘𝑟 ,
𝐼̅ =
𝑃 = 𝐼𝑉 ,
𝑅𝑒𝑞,𝑠𝑒𝑟𝑖𝑒𝑠 = 𝑅1 + 𝑅2 + ⋯,
�F⃗ = 𝐼𝑙⃗ × �B⃗ ,
B=
𝜇0 𝐼
2𝜋 𝑟
𝐵=
,
𝜀2 = −𝑀 𝑑𝐼1 ⁄𝑑𝑡 ,
𝑀=
𝑅
𝑄 = 𝑄0 𝑒 −2𝐿𝑡 cos(𝜔′ 𝑡 + 𝜙),
,
1
� 𝜀 0 𝜇0
3
2(𝑅 2 +𝑥2 )2
𝑁2 Φ21
𝐼1
𝐼 = 𝐼0 𝑒
1
𝑋𝐶 = 𝜔𝐶
𝑍 = �𝑅 2 + (𝑋𝐿 − 𝑋𝐶 )2
𝑐=
𝐼
𝑗=𝐴 ,
1
,
,
1
�⃗ ,
𝑆⃗ = 𝜇 𝐸�⃗ × 𝐵
0
Constants
𝑑Φ𝐵
,
𝑑𝑡
−𝑡�
𝜏
−1
2
𝐵 = 𝜇0 𝑛𝐼 ,
𝜀 = −𝐿 𝑑𝐼 ⁄𝑑𝑡 ,
𝜏 = 𝐿⁄𝑅 ,
𝐼 = 𝐼0 cos𝜔𝑡 ,
,
,
tan∅ =
𝑐 = λ𝑓 ,
1
𝐼𝑟𝑚𝑠 =
,
𝑉0 = 𝐼0 𝑋𝐿
𝑉𝐿0 −𝑉𝐶0
𝑉𝑅0
1 𝑐
𝑎𝑐 =
𝑣2
𝑟
𝐸0 𝐵0
2𝜇0
k = 9.0 × 109 N.m2/C2 ,
ε 0 = 8.85 × 10-12 C2/N.m2 ,
c = 3.00 × 108 m/s ,
e = 1.60 × 10-19 C ,
𝐹2 = 𝐵1 𝐼2 𝑙2
Φ𝐵
𝐼
U=
,
𝑄 = 𝑄0 cos(𝜔𝑡 + 𝜙),
𝐼0
√2
,
𝑉𝑟𝑚𝑠 =
�⃗
�⃗ = 𝑁𝐼A
µ
�⃗ ,
τ�⃗ = µ
��⃗× B
,
𝑉0
1
�⃗ =
𝑑𝐵
𝜇0 𝐼 𝑑𝑙⃗×𝑟̂
𝜀 = 𝐵𝑙𝑣
𝐿𝐼 2 ,
2
4𝜋
𝑢𝐵 =
𝑟2
1 𝐵2
2 𝜇0
1
𝜔 = 2𝜋𝑓 = �𝐿𝐶
√2
𝑋𝐿 = 𝜔𝐿 ,
𝑣 = 𝐸 ⁄𝐵
µ 0 = 4π × 10-7 T.m/A,
m e = 9.1 × 10-31 kg ,
10
𝑉𝑎𝑏 = 𝜀 − 𝐼𝑟
�⃗ . 𝑑𝐴⃗ = 0 ,
∮𝐵
𝐿=𝑁
𝑣 = 𝜔⁄𝑘 ,
0
,
2
𝑃� = 𝐼𝑟𝑚𝑠
𝑍cos∅
,
𝑆̅ = 2 𝜀0 𝑐𝐸02 = 2 𝜇 𝐵02 =
𝚥⃗ = 𝜎𝐸�⃗ , 𝜎 = 1�𝜌
𝑑Φ𝐵
∮ 𝐸�⃗ . 𝑑𝑙⃗ = − 𝑑𝑡 ,
,
,
2
𝚥⃗ = 𝑛𝑞𝑣
����⃗
𝑑 ,
1
1
𝑢𝐸 = 2 𝜀0 𝐸 2
,
𝐶
𝑑𝑉
𝐸𝑙 = − 𝑑𝑙
−1
1
1
�F⃗𝐿𝑜𝑟𝑒𝑛𝑡𝑧 = 𝑞�E
�⃗ + v
�⃗�,
�⃗ × B
𝜀 = −𝑁
𝐼 = 𝐼𝑚𝑎𝑥 �1 − 𝑒 −𝑡⁄𝜏 � ,
𝑉0 = 𝐼0 𝑋𝐶
1
𝑅𝑒𝑞,𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙 = �𝑅 + 𝑅 … �
𝜇0 𝐼𝑅 2
1 𝑄2
1
𝐶𝑒𝑞,𝑠𝑒𝑟𝑖𝑒𝑠 = �𝐶 + 𝐶 + ⋯ �
,
Δt
1
�⃗ . 𝑑𝑙⃗ = µ 𝐼 + µ 𝜀0 𝑑Φ𝐸 ,
∮𝐵
0
0
𝑑𝑡
∮ �B⃗. 𝑑𝑙⃗ = 𝜇0 𝐼𝑒𝑛𝑐𝑙 ,
�⃗
Φ𝐵 = ∫ �B⃗. 𝑑A
ΔQ
0
𝑏
∆𝑉 = − ∫𝑎 𝐸�⃗ . 𝑑𝑙⃗ ,
𝑈 = 2 𝑄𝑉 = 2 𝐶𝑉 2 = 2
1
�F⃗ = 𝑞v
�⃗ × �B⃗ ,
,
𝐴
∆𝑈 = 𝑞∆𝑉 ,
𝐶 = 𝐾𝜀0 𝑑 = 𝜀 𝑑 ,
𝐶𝑒𝑞,𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙 = 𝐶1 + 𝐶2 + ⋯ ,
𝑄
∮ 𝐸�⃗ . 𝑑𝐴⃗ = 𝑒𝑛𝑐𝑙
𝜀
ΦE = ∫ 𝐸�⃗ . 𝑑𝐴⃗ ,
𝐴
𝐶 = 𝜀0 𝑑 ,
𝑉 = 𝐼𝑅 ,
𝐹
𝐸�⃗ = 𝑞 ,
𝐸 = 𝑘 𝑟2 ,
𝑝 = 𝑄𝑙 ,
𝐶=𝑉 ,
⃗
𝑄
,
g = 9.8 m/s2
m p = 1.67 × 10-27 kg
College of Arts and Sciences
Department of Mathematics, Statistics, and Physics
Physics Program
General Physics for Engineering II
PHYS 193
Fall 2014
10th January 2015
FINAL EXAM
Instructors: Dr. A. Shalaby, Dr. A. Ayesh, and Dr. D. Abdulmalik
100
Student Name:
Student ID:
Section number:
Please read the following instructions carefully before you start answering
1. Make sure that you have 9 pages including two parts, A and B. Part A consists of 10 multiple choice
questions, and part B consists of 3 problems.
2. Calculators are permitted but no electronic dictionaries or mobile phones.
3. All your work must be done on your exam paper; no loose papers are allowed.
4. This is a timed exam (120 min). Do not spend too much time on any particular question.
Best Wishes
1
Part A. Please choose the one alternative that best completes the statement or
answers the question, circle your choice using pen and justify your choice.
60
Make sure that only ONE of the alternatives is chosen for each question. Two answers to one question will
result in loss of the mark of that question.
1.
Four point charges are located at the corners of a square of side a as shown in the figure below. The
magnitudes of the resulting electric field and the electric potential at the center of the square are
A.
B.
C.
D.
q
E = 0, 𝑉 = 4(√2)𝑘𝑒 𝑞⁄𝑎
𝐸 = 8𝑘𝑒 𝑞 ⁄𝑎2 , 𝑉 = 0
E = 0, 𝑉 = 0
𝐸 = 8𝑘𝑒 𝑞 ⁄𝑎2 , 𝑉 = 4(√2)𝑘𝑒 𝑞⁄𝑎
-q
a
Justification:
q
-q
2. A charge Q is uniformly spread over one surface of a very large non-conducting square sheet having
sides of length d. At a point P that is 1.25 cm outside the sheet, the magnitude of the electric field due
to the sheet is E. If the sheet is now stretched so that its sides have length 2d, what is the magnitude of
the electric field at P?
A. 4E
B. 2E
C. E
D. E/2
E. E/4
Justification:
2
3. The three points A, B, and C are located inside the uniform electric field, E as shown in the figure
below. Which statement is correct?
A.
B.
C.
D.
𝑉𝐴
𝑉𝐴
𝑉𝐴
𝑉𝐴
< 𝑉𝐵
> 𝑉𝐵
= 𝑉𝐵
> 𝑉𝐵
Justification:
= 𝑉𝐶
< 𝑉𝐶
> 𝑉𝐶
= 𝑉𝐶
4. When two or more capacitors are connected in series across a potential difference
A. each capacitor carries the same amount of charge.
B. the potential difference across the combination is the algebraic sum of the potential differences
across the individual capacitors.
C. the equivalent capacitor of the combination is less than the capacitance of any of the capacitors.
D. all of the above choices are correct.
E. none of the above choices is correct.
Justification:
5. A charged particle with a mass m is moving perpendicular to a magnetic field in a circle with radius r.
If we double the mass of the particle, the period (T) of one complete revolution will
A. halve
Justification:
B. quadruple
C. remain the same
D. double
3
6. A negatively charged particle is moving to the right, directly above a wire having a current flowing to
the right, as shown in the figure. In which direction is the magnetic force exerted on the particle?
A.
B.
C.
D.
E.
Into the page
Out of the page
Upward
Downward
The magnetic force is zero since the
velocity is parallel to the current.
Justification:
7. The figure below shows, in cross section, three conductors that carry currents through the plane of the
figure. The current have the magnitude I1 = 3.0 A, I2 = 6.0 A, and I3 = 2.0 A, in the directions shown.
�⃗ . ���⃗
Through which path the line integral ∮ 𝐵
𝑑𝑙 has the maximum value?
A. a
B. b
C. c
D. d
Justification:
8. Two very long, straight wires carry currents as shown in the figure. What are the locations where the
net magnetic field is zero?
A. (a) and (b)
B. (a) and (c)
Justification:
C. (a) and (d)
D. (b) and (c)
E. (b) and (d)
F. (c) and (d)
4
9. An insulated wire is wrapped tightly around a cylindrical core of radius 5.0 cm and length 30 cm to
build a 300-turn solenoid. What is the energy stored in this solenoid when a current I = 0.20 A flows
through it?
A.
B.
C.
D.
E.
9.6 × 10-4 J
4.8 × 10-4 J
2.4 × 10-4 J
1.2 × 10-4 J
5.9 × 10-5 J
Justification:
10. The figure shows a bar magnet moving vertically upward toward a horizontal coil. The poles of the
bar magnets are labeled X and Y. As the bar magnet approaches the coil it induces an electric current
in the direction indicated on the figure (counter-clockwise as viewed from above). What are the
correct polarities of the magnet?
A.
B.
C.
D.
E.
X is a south pole, Y is a north pole.
X is a north pole, Y is a south pole.
Both X and Y are north poles.
Both X and Y are south poles.
The polarities of the magnet cannot be determined from the given
information.
Justification:
5
Part B. Please solve the following problems using pen and showing all the steps
of your work in a clear tidy way.
40
1. A circular conducting ring of radius R is connected to two exterior wires as shown in the figure. The
�⃗ at the center of the
current I splits into unequal portions while passing through the ring. What is �𝐁
ring? (15 points)
6
2. A coil with 150 turn, 5.0 cm radius, and a resistance of 12 Ω surrounds a solenoid with 230 turns/cm
and a radius of 4.5 cm. The current in the solenoid changes at a constant rate from 0 to 2.0 A in
0.10
s. Find the magnitude of the induced current in the 150-turn coil. (10 points)
7
3. An inductor with an inductance of 2.50 H and a resistor of 8.00 Ω are connected to the terminals of a
battery with an emf of 6.00 V. Find:
A. The initial rate of increase of current in the circuit (di/dt at t = 0). (5 points)
B. The current at t = 0.250 s after the circuit is closed. (5 points)
C. The final steady-state current (Imax). (5 points)
8
Useful Formulae
|𝑄1 𝑄2 |
𝐹=𝑘
𝑄
𝐸�⃗ = 𝑘 𝑟 2 𝑟̂ ,
,
𝑟2
⃗
𝐹
𝐸�⃗ = 𝑞 ,
𝑄
Φ𝐸 = ∫ 𝐸�⃗ . 𝑑𝐴⃗ , ∮ 𝐸�⃗ . 𝑑𝐴⃗ = 𝑒𝑛𝑐𝑙
𝜀
𝑞
𝑉 =𝑘𝑟 , 𝑉 =
𝐶=
𝑄
𝑉
𝐼=
𝑑𝑄
𝑑𝑡
,
𝐶=
𝑈
𝑞
𝐴
𝜀0
𝑑
0
,
𝑈=
1
𝑄𝑉
2
=
𝑖
1
𝐶𝑉 2
2
=
1 𝑄2
2 𝐶
1
𝐶1
𝐶𝑒𝑞,𝑠𝑒𝑟𝑖𝑒𝑠 = � +
, 𝐼 = 𝑛|𝑞|𝑣𝑑 𝐴 , 𝑉 = 𝐼𝑅 , 𝑅 =
𝐼
𝐴
𝜌𝑙
𝐴
1
𝑅1
�⃗ , 𝐹⃗ = 𝐼𝑙⃗ × 𝐵
�⃗ ,
𝐹⃗ = 𝑞𝑣⃗ × 𝐵
𝜀 = −𝑁
U=
𝑑Φ𝐵
𝑑𝑡
1
𝐿𝐼 2
2
,
,
𝜇0 𝐼 𝑑𝑙⃗×𝑟̂
4𝜋 𝑟 2
1 𝐵2
2 𝜇0
𝑉2
𝑉1
𝑞 = 𝑄cos(𝜔𝑡 + 𝜙) ,
∮ 𝐸�⃗ . 𝑑𝐴⃗ =
𝑄𝑒𝑛𝑐𝑙
𝜀0
𝑎𝑐 =
�⃗ =
𝑑𝐵
𝜀2 = −𝑀
, 𝑢𝐵 =
1
𝐶2
1
−1
+ ⋯�
𝑉2
𝑅
, 𝚥⃗ = 𝜎𝐸�⃗ , 𝜎 = 1�𝜌 , 𝜌(𝑇) = 𝜌0 [1 + 𝛼(𝑇 − 𝑇0 )] ,
,
𝑑𝑖1
𝑑𝑡
,
=
,
𝑣2
𝑟
𝐵=
𝑀=
𝑁2
𝑁1
,
,
−1
1
…� ,
𝑅2
−𝑡
𝐼0 𝑒 �𝑅𝐶 ,
+
−𝑡
Charging Capacitor: 𝑞 = 𝑄𝑓 �1 − 𝑒 �𝑅𝐶 � , 𝑖 =
�⃗×𝑟̂
𝜇0 𝑞𝑣
4𝜋 𝑟 2
𝑝 = 𝑞𝑑
, 𝑢 = 2 𝜀0 𝐸 2
, 𝑃 = 𝐼𝑉 = 𝐼 2 𝑅 =
𝑅𝑒𝑞,𝑠𝑒𝑟𝑖𝑒𝑠 = 𝑅1 + 𝑅2 + ⋯, 𝑅𝑒𝑞,𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙 = �
�⃗ =
𝐵
𝑈 = −𝑝⃗ ∙ 𝐸�⃗ ,
𝑏
𝑞
𝜕𝑉
, 𝑈 = 𝑘𝑞0 Σ𝑖 𝑟 𝑖 , 𝑊𝑎→𝑏 = 𝑈𝑎 − 𝑈𝑏 , 𝑉𝑎 − 𝑉𝑏 = ∫𝑎 𝐸�⃗ . 𝑑𝑙⃗ , 𝐸𝑥 = − 𝜕𝑥
𝐶𝑒𝑞,𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙 = 𝐶1 + 𝐶2 + ⋯,
𝚥⃗ = 𝑛𝑞𝑣
����⃗
𝑑, 𝑗 =
𝜏⃗ = 𝑝⃗ × 𝐸�⃗ ,
�⃗ ,
𝜏⃗ = 𝜇⃗ × 𝐵
𝜇0 𝐼𝑅2
,
3
2(𝑅2 +𝑥 2 )2
𝑁2 ΦB2
𝑖1
,
𝑉𝑎𝑏 = 𝜀 − 𝐼𝑟
∑𝑗𝑢𝑛𝑐𝑡𝑖𝑜𝑛 𝐼 = 0 ,
−𝑡
−𝑡
Discharging Capacitor: 𝑞 = 𝑄0 𝑒 �𝑅𝐶 , 𝑖 = 𝐼0 𝑒 �𝑅𝐶
�⃗ ,
𝑈 = −𝜇⃗ ∙ 𝐵
𝜇 = 𝐼𝐴 ,
∮ �B⃗. 𝑑𝑙⃗ = 𝜇0 𝐼𝑒𝑛𝑐𝑙 ,
𝜀 = −𝐿
∑ 𝑙𝑜𝑜𝑝 𝑉 = 0
𝑑𝑖
𝑑𝑡
, 𝐿=𝑁
Φ𝐵
𝑖
𝜇0 𝐼
2𝜋 𝑟
B=
,
�⃗
Φ𝐵 = ∫ �B⃗. 𝑑A
𝐵 = 𝜇0 𝑛𝐼 ,
�⃗� ∙ 𝑑𝑙⃗
, 𝜀 = 𝐵𝑙𝑣 , 𝜀 = ∮�𝑣⃗ × 𝐵
𝑡
𝑉1 𝐼1 = 𝑉2 𝐼2 , 𝑖 = 𝐼�1 − 𝑒 −𝑡⁄𝜏 � , 𝑖 = 𝐼0 𝑒 − �𝜏 , 𝜏 = 𝐿⁄𝑅
𝑖 = −𝜔𝑄sin(𝜔𝑡 + 𝜙) ,
1
𝐿𝐶
𝜔=�
�⃗. 𝑑𝐴⃗ = 0 , ∮ B
�⃗. 𝑑𝑙⃗ = 𝜇0 𝐼𝑒𝑛𝑐𝑙 ,
, ∮𝐵
,
𝑐=
1
�𝜀0 𝜇0
,
𝑐 = 𝐸 ⁄𝐵
�⃗. 𝑑𝑙⃗ = µ 𝐼𝑒𝑛𝑐𝑙 + µ 𝜀0
∮𝐵
0
0
𝑑Φ𝐸
𝑑𝑡
,
∮ 𝐸�⃗ . 𝑑𝑙⃗ = −
𝑑Φ𝐵
𝑑𝑡
Useful Constants
k = 9.0 × 109 N.m2/C2 , ε0 = 8.85 × 10-12 C2/N.m2 , 𝜇0 = 4π×10−7 𝑇. 𝑚/A , c = 3.0 ×108 m/s
g = 9.8 m/s2 ,
e = 1.60 × 10-19 C ,
me = 9.1 × 10-31 kg ,
mp = 1.67 × 10-27 kg
9
College of Arts and Sciences
Department of Mathematics, Statistics, and Physics
Physics Program
General Physics for Engineering II
PHYS 193
Fall 2015
7th January 2016
FINAL EXAM
Instructors: Dr. A. Shalaby, Dr. A. Ayesh, Dr. D. Abdulmalik
100
Student Name:
Student ID:
Section number:
Please read the following instructions carefully before you start answering
1. Make sure that you have 9 pages including two parts, A and B. Part A consists of 10 multiple choice
questions, and part B consists of 3 problems.
2. Calculators are permitted but no electronic dictionaries or mobile phones.
3. All your work must be done on your exam paper; no loose papers are allowed.
4. This is a timed exam (120 min). Do not spend too much time on any particular question.
Best Wishes
1
Part A. Please choose the one alternative that best completes the statements or
answers the questions, circle your choice using pen and justify your choice.
50
Make sure that only ONE of the alternatives is chosen for each question. Two answers to one question will
result in loss of the mark of that question.
1.
When two point charges are a distance d part, the electric force that each one feels from the other has
magnitude F. In order to make this force twice as strong, the distance would have to be changed to
A.
B.
C.
D.
E.
2.
Justification:
Consider a spherical Gaussian surface of radius R centered at the origin. A charge Q is placed inside
the sphere. To maximize the magnitude of the flux of the electric field through the Gaussian surface,
the charge should be located
A.
B.
C.
D.
E.
3.
2d
𝑑⁄2
𝑑⁄√2
√2d
𝑑⁄4
at the origin
at x =0, y = 0, z = R/2
at x =0, y = R/2, z = 0
at x =R/2, y = 0, z = 0
anywhere inside the sphere
Justification:
Three negative charges of equal magnitudes are positioned along the x-axis at x = -a, x = 0, and x =
+a respectively. The charge located at x = 0 is moved away along the y-axis to a position (x, y) = (0,
+a). How does the potential energy of the system of charges change as a result of this move?
A.
B.
C.
D.
E.
The potential energy stays the same.
The potential energy increases.
The potential energy decreases.
The potential energy may increase or decrease depending on the magnitude of the charges.
More information is needed to answer the question.
Justification:
2
4.
A parallel-plate capacitor stores a charge Q = 4.00 nC when connected to a battery of 10 V. The
energy density is u = 3.62  10-4 J/m3. What is the surface area of the plates?
A.
B.
C.
D.
E.
5.
Justification:
A charge is accelerated from rest through a potential difference V and then enters a uniform magnetic
field oriented perpendicular to its path. The field deflects the particle into a circular arc of radius R.
If the accelerating potential is tripled to 3V, what will be the radius of the circular arc?
A.
B.
C.
D.
E.
6.
0.0103 m2
0.0250 m2
0.0387 m2
0.0500 m2
0.0923 m2
3R
𝑅 ⁄√3
√3𝑅
9R
R/9
Justification:
A hollow cylinder with an inner radius of 4.0 mm and an outer radius of 30 mm conducts a 3.0-A
current flowing parallel to the axis of the cylinder. If the current density is uniform throughout the
wire, what is the magnitude of the magnetic field at a point 12 mm from its center?
A.
B.
C.
D.
7.2 × 10-6 T
8.0 × 10-6 T
8.9 × 10-7 T
7.1 × 10-8 T
Justification:
3
7.
The figure shows three long parallel current-carrying wires. The current directions are indicated for
currents I1 and I3. The arrow labeled F represents the magnetic force acting on current I3. The 3
currents have equal magnitudes. What is the direction of the current I2?
A.
B.
C.
D.
E.
Out of the picture (in the same direction as I1 and I3)
Into the picture (in the direction opposite to I1 and I3)
Vertical upward
Vertical downward
Horizontal to the right
I3
I1
F
Justification:
8.
I2
A conducting bar slides without friction on two parallel horizontal rails that are 50 cm apart and
connected by a wire at one end. The resistance of the bar and the rails is constant and equal to 0.10
Ω. A uniform magnetic field is perpendicular to the plane of the rails. A 0.080-N force parallel to the
rails is required to keep the bar moving at a constant speed of 0.50 m/s. What is the magnitude of the
magnetic field?
A.
B.
C.
D.
E.
0.10 T
0.25 T
0.36 T
0.54 T
0.93T
Justification:
4
9.
A coil is tightly wound around the center of a 0.80 m-length solenoid. The coil's resistance is 9.9 
and the mutual inductance of the coil and solenoid is 31 μH. At a given instant, the current in the
solenoid is 540 mA, and is decreasing at the rate of 2.5 A/s. What is the magnitude of the induced
current in the coil at this instant?
A.
B.
C.
D.
E.
13 A
11 A
9.4 A
7.8 A
6.3 A
Justification:
10. When a current of 2.0 A flows in the 100-turn primary of an ideal transformer, this causes 14 A to
flow in the secondary. How many turns are in the secondary?
A.
B.
C.
D.
E.
4
14
114
356
700
Justification:
5
Part B. Please solve the following problems using pen and showing all the steps
of your work in a clear tidy way.
50
⃗ , at all points within a circular region of radius R = 2.50 cm, is uniform in
1. A The magnetic field 𝐵
space and directed as shown in figure. If the magnetic field is increasing at a rate of dB/dt = 2.00 T/s,
find the magnitude and direction of the electric force on a stationary positive point charge q = 4.00 C
located at;
a) point a, a distance r = 2.00 cm above the center of the region. (6 points)
b) point b, a distance r = 2.00 cm to the right of the center of the region. (6 points)
c) point c, at the center of the region. (3 points)
6
2. Consider the current-carrying loop shown in the figure, formed of radial lines and segments of circles
whose centers are at point P. Find the magnitude and direction of the magnetic field B at P. (15 point)
7
3. The switch in the circuit shown in the figure is first connected to point a for a long time. After that the
switch is connected to point b.
a) What is the frequency of the oscillation of the circuit? (4 points)
b) What is the maximum charge on the capacitor? (4 points)
c) What is the maximum current in the inductor? (4 points)
d) What is the total energy in the circuit at t = 3.00 s? ( 8 points)
8
Useful Formulae:
|𝑞1 𝑞2 |
𝐹=𝑘
𝑞
𝐸⃗ = 𝑘 𝑟 2 𝑟̂ ,
,
𝑟2
Φ𝐸 = ∫ 𝐸⃗ . 𝑑𝐴 , ∮ 𝐸⃗ . 𝑑𝐴 =
𝑞
𝑉 =𝑘𝑟 , 𝑉 =
𝐶=
𝑄
𝑉
𝑞
𝐼=
𝑈 = −𝑝 ∙ 𝐸⃗ ,
𝑄𝑒𝑛𝑐𝑙
𝜀0
1
2
1
2
𝑈 = 𝑄𝑉 = 𝐶𝑉 2 =
,
1 𝑄2
2 𝐶
1
, 𝑢 = 2 𝜀0 𝐸 2
1
1
1
2
−1
𝐶𝑒𝑞,𝑠𝑒𝑟𝑖𝑒𝑠 = (𝐶 + 𝐶 + ⋯ )
, 𝐼 = 𝑛|𝑞|𝑣𝑑 𝐴 , 𝑉 = 𝐼𝑅 , 𝑅 =
𝜌𝑙
𝐴
, 𝑃 = 𝐼𝑉 = 𝐼 2 𝑅 =
𝑉2
𝑅
𝐼
𝑗 = 𝑛𝑞𝑣
⃗⃗⃗⃗𝑑 , 𝑗 = 𝐴 , 𝑗 = 𝜎𝐸⃗ , 𝜎 = 1⁄𝜌 , 𝜌(𝑇) = 𝜌0 [1 + 𝛼(𝑇 − 𝑇0 )] ,
1
𝑅1
𝑅𝑒𝑞,𝑠𝑒𝑟𝑖𝑒𝑠 = 𝑅1 + 𝑅2 + ⋯, 𝑅𝑒𝑞,𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙 = (
+
−1
1
…) ,
𝑅2
⃗ , 𝐹 = 𝐼𝑙 × 𝐵
⃗ ,
𝐹 = 𝑞𝑣 × 𝐵
⃗ ×𝑟̂
𝜇0 𝑞𝑣
4𝜋 𝑟 2
𝜀 = −𝑁
U=
𝑑𝐵
𝑑𝑡
1
𝐿𝐼 2
2
⃗ =
𝑑𝐵
,
𝜇0 𝐼 𝑑𝑙 ×𝑟̂
4𝜋 𝑟 2
𝜀2 = −𝑀
,
, 𝑢𝐵 =
1 𝐵2
2 𝜇0
,
𝑎𝑐 =
𝑑𝑖1
𝑑𝑡
𝑉2
𝑉1
𝑀=
𝑁2
𝑁1
,
⃗ ,
𝜏 = 𝜇×𝐵
,
𝐵=
,
,
=
𝑣2
𝑟
𝜇0 𝐼𝑅2
,
3
2(𝑅2 +𝑥 2 )2
𝑁2 B2
𝑖1
,
⃗ . 𝑑𝑙 = 𝜇0 𝐼𝑒𝑛𝑐𝑙 ,
∮B
𝑑𝑖
1
√𝜀0 𝜇0
⃗
⃗ . 𝑑A
𝐵 = ∫ B
⃗ ,
𝑈 = −𝜇 ∙ 𝐵
𝜇 = 𝐼𝐴 ,
𝑐=
∑ 𝑙𝑜𝑜𝑝 𝑉 = 0
−𝑡
−𝑡
Discharging: 𝑞 = 𝑄0 𝑒 ⁄𝑅𝐶 , 𝑖 = 𝐼0 𝑒 ⁄𝑅𝐶
𝜀 = −𝐿 𝑑𝑡 , 𝐿 = 𝑁
𝑉1 𝐼1 = 𝑉2 𝐼2 ,
𝑉𝑎𝑏 = 𝜀 − 𝐼𝑟
∑𝑗𝑢𝑛𝑐𝑡𝑖𝑜𝑛 𝐼 = 0 ,
−𝑡
−𝑡
R-C Circuit: Charging: 𝑞 = 𝑄𝑓 (1 − 𝑒 ⁄𝑅𝐶 ) , 𝑖 = 𝐼0 𝑒 ⁄𝑅𝐶 ,
⃗ =
𝐵
𝑝 = 𝑞𝑑
𝑖
𝐶𝑒𝑞,𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙 = 𝐶1 + 𝐶2 + ⋯,
𝑑𝑄
𝑑𝑡
𝜏 = 𝑝 × 𝐸⃗ ,
𝑏
𝑞
𝜕𝑉
, 𝑈 = 𝑘𝑞0 Σ𝑖 𝑟 𝑖 , 𝑊𝑎→𝑏 = 𝑈𝑎 − 𝑈𝑏 , 𝑉𝑎 − 𝑉𝑏 = ∫𝑎 𝐸⃗ . 𝑑𝑙 , 𝐸𝑥 = − 𝜕𝑥
𝑈
𝐴
𝑑
𝐶 = 𝜀0
,
𝐹
𝐸⃗ = 𝑞 ,
𝐵
𝑖
B=
𝜇0 𝐼
2𝜋 𝑟
,
𝐵 = 𝜇0 𝑛𝐼 ,
⃗ ) ∙ 𝑑𝑙
, 𝜀 = 𝑣𝐵𝑙 , 𝜀 = ∮(𝑣 × 𝐵
𝐸 = 𝑐𝐵
,
𝑡
R-L Circuit : 𝑖 = 𝐼(1 − 𝑒 −𝑡⁄𝜏 ) , = 𝐼0 𝑒 − ⁄𝜏 , 𝜏 = 𝐿⁄𝑅 ,
L-C Circuit : 𝑞 = 𝑄cos(𝜔𝑡 + 𝜙) ,
∮ 𝐸⃗ . 𝑑𝐴 =
𝑄𝑒𝑛𝑐𝑙
𝜀0
,
⃗ . 𝑑𝐴 = 0 ,
∮𝐵
𝑖 = −𝜔𝑄sin(𝜔𝑡 + 𝜙) ,
⃗ . 𝑑𝑙 =  𝐼𝑒𝑛𝑐𝑙 +  𝜀0
∮𝐵
0
0
1
𝜔 = √𝐿𝐶
𝑑𝐸
𝑑𝑡
,
∮ 𝐸⃗ . 𝑑𝑙 = −
𝑑𝐵
𝑑𝑡
Useful Constants:
k = 9.0  109 N.m2/C2 , 0 = 8.85  10-12 C2/N.m2 , 𝜇0 = 4π×10−7 𝑇. 𝑚/A , c = 3.0 ×108 m/s
g = 9.8 m/s2 ,
e = 1.60  10-19 C ,
me = 9.1  10-31 kg ,
mp = 1.67  10-27 kg
9
College of Arts and Sciences
Department of Mathematics, Statistics, and Physics
Physics Program
General Physics for Engineering II
PHYS 193
Spring 2016
9th June 2016
FINAL EXAM
Instructors: Dr. Ahmad Ayesh & Dr. Mohammad Gharaibeh
Student Name:
100
Student ID:
Section number:
List Number:
Please read the following instructions carefully before you start answering
1. Make sure that you have 9 pages including two parts, A and B. Part A consists of 10 multiple choice
questions, and part B consists of 3 problems.
2. Calculators are permitted but no electronic dictionaries or mobile phones.
3. All your work must be done on your exam paper; no loose papers are allowed.
4. This is a timed exam (120 min). Do not spend too much time on any particular question.
Best Wishes
1
Useful Formulae:
|
|
Φ
̂ ,
,
.
,
Σ
,
,
,
→
,
,
,
⋯,
,
| |
,
,
.
,
,
1
1
̂
,
,
1
B2
L‐C Circuit :
cos
,
0 ,
∮ .
,

,

,
B
B. A
,
,
∮
,
∙
,
⁄
,
sin
,
∮ .
,
,
,
0
∙
∮ B.
,
,
∑
Discharging:
,
,
,
⁄
0 ,
,
,
,
R‐L Circuit :
,
,
,
∑
,
,
,
,
1
…
,
,
,
,
R‐C Circuit: Charging:
∮ .
,
,
⋯,
̂
⋯
,
,
,
,
,
,
U
,
, ∮ .
,

∙
,
,



∮ .
,

Useful Constants:
k = 9.0  109 N.m2/C2 , 0 = 8.85  10‐12 C2/N.m2 ,
g = 9.8 m/s2 ,
e = 1.60  10‐19 C ,
0
4π 10
7
me = 9.1  10‐31 kg ,
.
/A , c = 3.0 ×108 m/s
mp = 1.67  10‐27 kg
2
Part A. Please choose the one alternative that best completes the statements or
answers the questions, circle your choice using pen and justify your choice.
50
Make sure that only ONE of the alternatives is chosen for each question. Two answers to one question will result
in loss of the mark of that question.
1. Two equal charges, each +4Q, are separated by some distance. What third charge would be needed to
be placed half way between the two charges so that the net force on each charge would be zero.
A) –Q/2
B) –Q
C) –Q/4
D) –Q/8
2. The electric field in space is given by E = (24iˆ  30 ˆj  16kˆ) N/C. What is the electric flux (in N.m2/C)
through a 2 m2 portion of the xy- plane
A) 48
B) 42
C) 34
D) 32
3. Point charges q and Q are positioned as shown. If q = +3.5nC, Q = -3.5nC , a = 3m, and b = 4m,
What is the electric potential difference |VA – VB|?
A) 8.4 V
q
B) 6.0 V
a
C) 7.2 V
A
D) 4.8 V
b
B
Q
a
3
44. A paralleel plate capaacitor of surrface chargee density σ = 50 μC/m2 filled with cartoon of ddielectric
constant κ = 1.41. Fin
nd the energ
gy stored perr unit volumee (J/m3).
A) 28
B) 14
C) 100
D) 7
55. A wire of
o 2 mm2 crross-sectionaal area and 10.3
1
cm lonng contains 2 ×1020 elecctrons. It has a 10 Ω
resistance. What is th
he drift veloccity of the charges in the w
wire when 5 volts batteryy is applied aacross it?
-4
A) 2 ×10
0 m/s
B) 7.8 ×10-4 m/s
C) 1.6 ×10-3 m/s
D) 3.9 ×10-4 m/s
66. The power dissipated
d in the 4 Ω resistor
r
is
A) 14.2 W
B) 4 W
C) 1.33 W
D) 28.4 W
4
7. What is the potential difference Vd – Va shown in the circuit below.
A) -8 V
B) 8 V
C) -10 V
D) 10 V
8. A magnetic field CANNOT:
A) change the kinetic energy of a charged particle
B) change the velocity of a charged particle
C) change the momentum of a charged particle
D) exert a force on a charged particle
9. A proton travels through a potential difference of 1 kV and then moves into a magnetic field of 0.03 T.
What is the radius of the proton resulting orbit?
A) 0.23 m
B) 0.15 m
C) 0.11 m
D) 0.08 m
5
110. In the arrrangement sh
hown, a con
nducting bar of negligiblle resistance slides alongg horizontal,, parallel,
frictionleess conductin
ng rails conn
nected as sho
own to a 2-
 resistor. A uniform 1.5-T magnetiic field is
perpendicular to the plane of thee paper. If L = 60 cm, att what is thee thermal poower being ddissipated
in the ressistor at the instant
i
the sp
peed of the bar
b is equal tto 4.4 m/s?
A) 8.6 W
B) 7.8 W
2
C) 7.1 W
D) 9.3 W
6
P
Part B. Pleease solve the follow
wing probllems usingg pen and showing aall the stepps
oof your wo
ork in a cleear tidy wa
ay.
50
11. The loop
p of wire sho
own in the figure
f
formss a right triaangle and caarries a current I = 500 A in the
direction
n shown. Thee loop is in a uniform maagnetic fieldd that has maagnitude B = 3.00 T and the same
direction
n as the curreent in the sid
de PQ of the loop.
((a) Find the magnitude
m
and
a direction
n of the force exerted by tthe magneticc field on eacch side of thee triangle.
(7 points)
((b) What is the
t net force on the loop? (2 points)
((c) The loop is pivoted ab
bout an axis that lies alon
ng the side P
PR, what is thhe magnitudde of the net ttorque on
the loop?? (6 points))
((d) Is the nett torque direccted to rotatee point Q intto the plane oof the figuree or out of the plane of thhe figure?
(2 poin
nts)
7
2. Two insulated wires perpendicular to each other in the same plane carry currents as shown in the
figure. Find the magnitude and direction of the net magnetic field these wires produce at points P. (16
points)
8
3. A long, thin solenoid has 900 turns per meter and radius 2.50 cm. The current in the solenoid is
increasing at a uniform rate of 60.0 A/s.
(a) What is the magnitude of the induced electric field at a point near the center of the solenoid and 0.500
cm from the axis of the solenoid (9 points)
(b) What is the self-inductance of this solenoid for 1.5 m length. (8 points)
9
College of Arts and Sciences
Department of Mathematics, Statistics, and Physics
Physics Program
General Physics for Engineering II
PHYS 193
Fall 2016
5th January 2017
FINAL EXAM
Instructors: Dr. D. Al-Abdulmalik, Dr. A. Shalaby Dr. M. Gharaibeh
Student Name:
100
Student ID:
Section Number:
List Number:
Please read the following instructions carefully before you start answering
1. Make sure that you have 8 pages including two parts, A and B. Part A consists of 10 multiple choice
questions, and part B consists of 3 problems.
2. Calculators are permitted but no electronic dictionaries or mobile phones.
3. All your work must be done on your exam paper; no loose papers are allowed.
4. This is a timed exam (120 min). Do not spend too much time on any particular question.
Best Wishes
1
Useful Formulae:
|
|
Φ
̂ ,
,
.
,
∙
,
.
,
,
, ∮ .
,
Σ
,
,
,
→
,
,
,
⋯,
,
| |
,
,
,
,
,
1
,
⋯,
,
…
1
,
̂
,
∑
,
,
,
,
,
,
1
,
R‐C Circuit: Charging:
̂
⋯
,
,
,
,
0 ,
,
∙
,
∮ B.
,
0
Discharging:
,
,
∑
,

,
B
B. A
,
,

sin
,
B2
,
U
,

,
,
∙
∮
,
,
R‐L Circuit :
1
L‐C Circuit :
cos
∮ .
,
,
,
⁄
,
0 ,
,
sin
,
∮ .
⁄
,
∮ .
,


2 /
,

∮ .
,
,

Useful Constants:
k = 9.0  109 N.m2/C2 , 0 = 8.85  10‐12 C2/N.m2 ,
g = 9.8 m/s2 ,
e = 1.60  10‐19 C ,
0
4π 10
7
me = 9.1  10‐31 kg ,
.
/A , c = 3.0 ×108 m/s
mp = 1.67  10‐27 kg
2
Part A. Please choose the one alternative that best completes the statements or
answers the questions, circle your choice using pen.
36
Make sure that only ONE of the alternatives is chosen for each question. Two answers to one question will result
in loss of the mark of that question.
1)
In the figure Q = 5 nC. What is the magnitude of the force on the charge Q?
A) 3.43 × 10-3 N
B) 1.56 × 10-3 N
C) 2.18 × 10-3 N
D) 1.80 × 10-3 N
E) 2.81 × 10-3 N
2)
Two imaginary spherical surfaces of radius R and 2R respectively surrounded a positive point
charge Q located at the center of the concentric spheres. When compared to the number of the field
lines N1 going through the sphere of radius R, the number of electric field lines N2 going through the
sphere of radius 2R is
A) N2 = ¼ N1
B) N2 = ½ N1
C) N2 = 4N1
D) N2 = 2 N1
E) N2 = N1
3)
Two parallel conducting plates are separated by 1 mm and carry equal but opposite surface charge
densities. If the potential difference between them is 3 V, what is the magnitude of the surface
charge density on each plate?
A) 26.55 nC/m2
B) 18.00 nC/m2
C) 44.25 nC/m2
D) 35.40 nC/m2
E) 53.10 nC/m2
3
4)
A wire carries a 4 A current along the +x-axis through a magnetic field
wire experiences a force of 10 N
A) 1.1 m
B) 0.87 m
C) 1.5 m
D) 0.50 m
E) 0.36 m
= (5.0 î + 7.0 ĵ) T. If the
as a result, how long is the wire?
5)
Two long parallel wires are placed side-by-side on a horizontal table. If the wires carry current in
opposite directions
A) one wire is lifted slightly as the other is forced against the table's surface
B) the wires attract each other
C) the wires repel each other
D) both wires are forced against the table's surface
E) both wires are lifted slightly
6)
A point charge Q moves on the x-axis in the positive direction with a speed of 370 m/s. A point P is
on the y-axis at y = +80 mm. The magnetic field produced at point P, as the charge moves through
the origin, is equal to -0.4 μT . When the charge is at x = +40 mm, what is the magnitude of the
magnetic field at point P?
A) 0.57 μT
P X
B) 0.74 μT
C) 0.14 μT
80 mm
D) 0.29 μT
Q
E) 1.3 μT
40 mm
7)
As shown in the figure, a wire and a 10 Ω resistor are used to form a circuit in the shape of a square,
20 cm by 20 cm. A uniform but non-steady magnetic field is directed into the plane of the circuit.
The magnitude of the magnetic field is decreased from 1.5 T to 0.5 T in a time interval of 10 ms. The
average induced current and its direction through the resistor, in this time interval, are closest to
A) 63 mA, from b to a.
B) 400 mA, from a to b.
C) 63 mA, from a to b.
D) 400 mA, from b to a.
E) 80 mA, from a to b.
4
8)
A rectangular coil having N turns and measuring 7 cm by 25 cm is rotating in a uniform 1 T
magnetic field with a frequency of 50 Hz. The rotation axis is perpendicular to the direction of the
field. If the coil develops a sinusoidal emf of maximum value 22 V, what is the value of N?
A) 5
B) 4
C) 2
D) 3
E) 1
9)
How much energy is stored in a room 3 m by 4 m by 2.1 m due to the earth's magnetic field with a
strength of 5.0 × 10-5 T?
A) 29.0 mJ.
B) 27.5 mJ.
C) 25.1 mJ.
D) 29.8 mJ.
E) 32.2 mJ.
10) At what rate would the current in a 100 mH inductor have to change to induce an emf of 0.1 V?
A)
B)
C)
D)
E)
1 A/s
10,000 A/s
100 A/s
10 A/s
1000 A/s
5
Part B. Please solve the following problems using pen and showing all the steps
of your work in a clear tidy way.
64
1) (20 points) A wire, in a plane, has the shape shown in the figure, two arcs of a circle connected by

radial lengths of wire. Determine B at point C in terms of R1 , R2 ,  , and the current I.
6
2) (22 points) A long, thin solenoid has 700 turns per meter and radius 2.5 cm. The current in the
solenoid is increasing at a uniform rate of 70 A/s. What is the magnitude of the induced electric field at
a point near the center of the solenoid and (a) 1.5 cm from the axis of the solenoid; (b) 2 cm from the
axis of the solenoid?
7
3) A capacitor with capacitance 5 × 10-5 F is charged by connecting it to a 10 V battery. The capacitor is
disconnected from the battery and connected across an inductor with 2 H inductance.
(a) What is the period of the electrical oscillations? (4 points)
(b) How much energy is initially stored in the capacitor? (4 points)
(c) What is the charge on the capacitor 0.02 s after the connection to the inductor is made? (6 points)
(d) At the time given in part (c), what is the current in the inductor? (4 points)
(e) At the time given in part (c), how much electrical energy is stored in the capacitor and how much is
stored in the inductor? (4 points)
8