Physics 227 – Hourly Exam 1
Thursday, October 1, 2015, 9:50 PM - 11:10 PM
ARC-103 (Aaa-Hoz), Hill 114 (Hua-Moz), PLH
(Mua-Shz), SEC 111 (Sia-Zzz)
Your name sticker
with exam code
⇒
SIGN HERE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
Use a #2 pencil to make entries on the answer sheet. Enter the following
ID information now, before the exam starts.
In the section labeled NAME (Last, First, M.I.) enter your last
name, then fill in the empty circle for a blank, then enter your
first name, another blank, and finally your middle initial.
Under STUDENT # enter your 9-digit RUID Number.
Under CODE enter the exam code given above.
Enter 227 under COURSE. You do not need to write anything else on the
answer sheet for now, but you may continue to read the instructions.
During the exam, you are allowed one 8.5 x 11 inch sheet of paper with
whatever you want written on it. NO Calculators. NO Cell phones.
The exam consists of 16 multiple-choice questions. For each multiple-choice
question mark only one answer. There is no deduction of points for an
incorrect answer, so even if you cannot work out the answer to a question,
you should make an educated guess.
If you have questions or problems during the exam, you may raise your
hand and a proctor will assist you. We will provide the value of physical
constants that are needed. It is your responsibility to know the relevant
equations.
A proctor will check your name sticker and your student ID sometime during
the exam. Please have them ready.
You are not allowed to help any other student, ask for help from anyone
but a proctor, change your seat without permission from a proctor or use
any electronic device. Doing so will result in a zero score for the exam.
When you are done with the exam, hand in only this cover sheet
and your answer sheet.
Please sign above by the name sticker to indicate that you have
read and understood these instructions.
Possibly useful constants:
ϵ0 = 1/µ0 c2 = 8.85 × 10−12 C2 /N·m2
k = 1/4πϵ0 = 8.99 × 109 N·m2 /C2
c = speed of light = 3.00 × 108 m/s
−qelectron = qproton = 1.602 × 10−19 C
melectron = electron mass = 9.11 × 10−31 kg
mproton = proton mass = 1.67 × 10−27 kg
1 eV = 1.602 × 10−19 J
Circumference of a circle =2πr; area of a circle is πr 2
Surface area of a sphere = 4πr 2 ; Volume of a sphere = 43 πr 3
Surface area of a cylinder = 2πrh + 2πr 2 ; Volume of cylinder = πr 2 h
sin(0◦ )= cos(90◦ ) = 0
sin(90◦ )= cos(0◦ ) = 1
sin(30◦ )= cos(60◦ ) =√
1/2
◦
◦
sin(60 )=cos(30 ) = √3/2
sin(45◦ )= cos(45◦ ) = 2/2
dxn
= nxn−1
!
!dx n
1
xn+1 except when n = −1. For n = −1, dx/x = lnx
x = n+1
Some metric prefixes:
f = femto = 10−15
p = pico = 10−12
n = nano = 10−9
µ = micro = 10−6
m = milli = 10−3
k = kilo = 103
M = mega = 106
G = giga = 109
1.
A positive point charge +Q is released from rest along the electric field line.
For the situation shown in the figure, which of the following statements is
TRUE?
a) The particle speeds up, in the direction of E.
b) The particle slows down, opposite to
the direction of E.
c) The particle slows down, in the direction of E.
d) The particle stays at the same speed.
e) Not enough information is given to
determine the particle’s speed.
2.
The figure displays five surfaces and a collection of positive and negative
charges all of the same magnitude Q. Rank the electric flux Φ through the
surfaces.
a)
b)
c)
d)
e)
3.
Φ1
Φ3
Φ1
Φ1
Φ3
>
>
=
>
=
Φ2
Φ1
Φ6
Φ2
Φ1
>
>
>
>
=
Φ3
Φ6
Φ3
Φ4
Φ6
>
>
>
=
>
Φ4
Φ2
Φ4
Φ5
Φ2
>
>
=
>
>
Φ5
Φ5
Φ5
Φ6
Φ4
>
=
>
>
>
Φ6
Φ4
Φ2
Φ3
Φ5
Four equal charges q are arranged at the corners of a square where the
length of each side is a. What is the potential energy UE of one of these
charges in the electric field due to the other 3 charges? Note: k = 1/4πϵ0 .
a)
b)
c)
d)
e)
UE
UE
UE
UE
UE
=
=
=
=
=
3kq 2 /a √
3kq 2 /(a 2)
√
2kq 2 /a + kq 2 /(a√2)
kq 2 /a +√ 2kq 2 /(a 2)
2kq 2 /(a 2)
4.
The capacitors in the network shown in the figure all have a capacitance
of C = 5.0 µF. What is the equivalent capacitance, Cab of this capacitor
network?
a)
b)
c)
d)
e)
Cab
Cab
Cab
Cab
Cab
=
=
=
=
=
5.0 µF
10.0 µF
20.0 µF
3.0 µF
1.0 µF
5.
Consider a conductor in electrostatic equilibrium. Which of the following
statements is FALSE?
a) Any net charge on the conductor must reside on the surface.
b) The electric field at the surface cannot have a component parallel to
the surface
c) No work is done by the electric field in moving a charge on the
surface.
d) The conductor cannot be given a net charge.
e) The electric potential must be constant inside the conductor.
6.
In the figure, an electric dipole has its dipole moment oriented at an angle
θ = 30 degrees with respect to the y axis. There is a uniform external
electric field of magnitude E = 2 N/C pointing in the +y direction. The
positive and negative ends of the dipole have charges of magnitude +q =
1 µC and the two charges are a distance d = 10 cm apart. The dipole is
free to rotate about a pivot through its center. What is the magnitude of
the torque τ that the electric field exerts about the center of mass of the
dipole?
a)
b)
c)
d)
e)
τ
τ
τ
τ
τ
=√
2 × 10−7 N·m
= 3 × 10−7 N·m
=√
1 × 10−7 N·m
= 3 × 10−5 N·m
= 1 × 10−6 N·m
7.
A conductor with a cavity carries a total charge of Qtotal = +7 nC. Within
the cavity, insulated from the conductor, is a point charge of Qpoint =
−5 nC. How much charge Qouter is on the outer surface of the outer conductor?
a)
b)
c)
d)
e)
8.
= +7 nC
= +2 nC
= +5 nC
= +12 nC
= −5 nC
In the figure there are two point charges +q (on the left) and −q (on the
right). There are also six positions, labeled A through F at various distances
from the two point charges. Rank the electric potentials V at points A to
F.
a)
b)
c)
d)
e)
9.
Qouter
Qouter
Qouter
Qouter
Qouter
VB
VB
VA
VB
VE
=
>
>
>
>
VE
VA
VB
VA
VF
>
>
>
>
>
VA
VE
VC
VC
VC
=
>
=
=
=
VF
VF
VD
VD
VD
>
>
>
>
>
VC
VD
VE
VF
VB
=
>
>
>
>
VD
VD
VF
VE
VA
The electrical energy density between the plates of a parallel plate capacitor
stays the same when the dimensions of the capacitor (length, width, and
plate separation) are all doubled. What is the ratio of the final stored
energy Uf to the inital stored energy Ui ?
a)
b)
c)
d)
e)
Uf /Ui
Uf /Ui
Uf /Ui
Uf /Ui
Uf /Ui
=
=
=
=
=
1
1/2
8
4
2
10.
What is the force F between a charged plastic insulator and a neutral
metal conductor?
a) F = 0
b) F is repulsive
c) F is attractive for positive-charged plastic, repulsive for negative
charged.
d) F is attractive for negative-charged plastic, repulsive for positive
charged.
e) F is attractive
11.
Two long straight parallel lines, A and B, carry uniform positive linear
charge densities. The charge density on line B is twice as great as the linear
charge density on line A, i.e., λB = 2λA . Where is the electric field due
to these lines equal to zero?
a) The electric field is zero along a line between the lines, closer to line
B than line A.
b) The electric field is zero along a line exactly midway between lines
A and B.
c) The electric field is zero along a line perpendicular to lines A and B.
d) There is no point at which the electric field is zero.
e) The electric field is zero along a line between the lines, closer to line
A than line B.
12.
An electric field does work Wab = 100 µJ moving a charge q = −0.1 µC
from point A to point B. Which of the following is TRUE?
a)
b)
c)
d)
e)
13.
The potential at point A is 1000 V lower than at point B.
The potential at point A is 1000 V higher than at point B.
The potential at point A is 100 µJ lower than at point B.
The potential at point A is 100 µJ higher than at point B.
The magnitude of the potential difference between points A and B is
1000 V, but depending on convention, the potential at point A can
be at a lower or higher voltage than at point B.
A 6.0 µF air-filled capacitor is connected across a 100-V voltage source.
After the source fully charges the capacitor, the capacitor is immersed in oil
with dielectric constant K=4. How much ADDITIONAL charge ∆Q flows
from the voltage source, which remained connected to the capacitor during
the entire time?
a)
b)
c)
d)
e)
∆Q
∆Q
∆Q
∆Q
∆Q
=
=
=
=
=
1.8
2.4
1.8
2.4
0.6
mC
mC
µC
µC
mC
14.
Two point charges lie along the x-axis: q1 = +4 C at x1 = 2 m and
q2 = +9 C at x2 = −3 m, What is electric field E⃗o at the origin? Use
k = 9 × 109 N·m2 /C2 .
a)
b)
c)
d)
e)
15.
E⃗o
E⃗o
E⃗o
E⃗o
E⃗o
=
=
=
=
=
+ 9 × 109 N/C ı̂
0
− 18 × 109 N/C ı̂
+ 18 × 109 N/C ı̂
− 9 × 109 N/C ı̂
A solid nonconducting sphere of radius R carries a uniform charge density
ρ throughout its volume. At a radial distance r1 = R/4 from the center,
the electric field has a magnitude of E1 = E0 . What is the magnitude of
the electric field E2 at a radial distance r2 = 2R?
a)
b)
c)
d)
e)
E2
E2
E2
E2
E2
=
=
=
=
=
E0
zero.
E0 /2
E0 /4
2E0
16.
The graph in the figure shows the variation of the electric potential V
(measured in volts) as a function of the radial direction r (measured in
⃗ is TRUE?
meters). Which statement about the electric field E
a) The magnitude of E
in the +r direction.
b) The magnitude of E
in the −r direction.
c) The magnitude of E
in the +r direction.
d) The magnitude of E
in the −r direction.
e) The magnitude of E
in the −r direction.
is largest from r = 0 m to r = 3 m and it is
is largest from r = 0 m to r = 3 m and it is
is largest from r = 3 m to r = 4 m and it is
is largest from r = 3 m to r = 4 m and it is
is largest from r = 4 m to r = 6 m and it is