Second Exam, 2014, no solutions

Physics 227 – Hourly Exam 2
Thursday, November 13, 2014, 9:50 PM - 11:10 PM
ARC-103 (Aaa-Gzz), PLH (Haa-Lzz),
LSH Aud (Maa-Rnn), BE Aud (Roa-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 wil provide the value of a 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
µ0 = 4π × 10−7 T·m/A = 12.57 × 10−7 T·m/A
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
x = n+1
xn+1 except when n = −1. For n = −1, dx/x = lnx
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.
You have two wires of the same length but made of diﬀerent materials.
Wire 1 has diameter d1 =4 mm and is made of a material with resistivity
ρ1 = 4 × 108 Ω-m. Wire 2 has diameter d2 =8 mm. If the resistance of the
two wires is the same, what is the resistivity ρ2 of material 2?
a)
b)
c)
d)
e)
2.
= 1 × 108 Ω-m.
= 2 × 108 Ω-m.
= 4 × 108 Ω-m.
= 8 × 108 Ω-m.
= 16 × 108 Ω-m.
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)
b)
c)
d)
e)
3.
ρ2
ρ2
ρ2
ρ2
ρ2
t = RC
t = RC/5
t = [RCln(5)]/2
t = RCln(5)
t = 2RCln(5)
⃗ Which of
A wire of length L is in a region of uniform magnetic field B.
the following statements about the force F⃗ is TRUE?
I. If the current in the wire flows straight down and the magnetic field
points due west, the force II. If the current in the wire flows due east and
the magnetic field points straight down, the forc III. If the current in the
wire flows due west and slightly up and the magnetic field points due ea
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.
4.
Which of the following equations implies that you get a greater EMF the
faster you rotate the coils of a generator?
a)
b)
c)
d)
e)
5.
A person with a body resistance between her hands of R1 accidentally
grasps the terminals of a power supply with EMF = E and internal resistance R2 . What is the power P dissipated in her body?
a)
b)
c)
d)
e)
6.
⃗ + ⃗v × B)
⃗
F⃗ = q(E
"
⃗ · dA
⃗ = q/ϵ0
E
"
⃗ · d⃗ℓ = −dΦB /dt
E
"
⃗ · dA
⃗=0
B
"
⃗
⃗
B · dℓ = µ0 I + µ0 ϵ0 (dΦE /dt)
P
P
P
P
P
= R1 E/(R1 + R2 )
= E 2 /R1
= E 2 /(R1 + R2 )
= R1 E 2 /(R1 + R2 )2
= (R1 + R2 )E 2 /R1 R2
You are given a circuit with two batteries each with EMF=E and internal
resistance R1 . They are connected in parallel to each other and then in
series to a resistor with resistance R2 , as shown in the figure. What is the
current I flowing through the resistor R2 ?
a)
b)
c)
d)
e)
I
I
I
I
I
= 2E/(2R1 + R2 )
= 2 E/(R1 + 2R2 )
= E/(2R1 + R2 )
= E/(R1 + 2R2 )
= 2ER1 R2 /(R1 + R2 )
7.
In the figure you are given two wires. Wire 1 carries a current I and wire 2
carries a current 2I. The point D is located a distance d below wire 1 and
the same distance d above wire 2. What are the magnitude and direction
⃗ at D?
of the magnetic field B
⃗ =0
a) B
⃗ = µ0 I/2πd, into the paper.
b) B
⃗ = µ0 I/2πd, out of the pac) B
per.
⃗ = µ0 I/πd, into the paper.
d) B
⃗ = µ0 I/πd, out of the paper.
e) B
8.
As shown in the figure, a metal rail with a sliding rod is in a uniform,
constant magnetic field B directed out of the plane of the paper. The rod
is sliding at speed v as shown. If the resistance of the assembly is R, what
will be the induced current?
B
a)
b)
c)
d)
e)
Zero
Bav/R clockwise
Bav/R counterclockwise
Bbv/R clockwise
Bbv/R counterclockwise
v
b
a
9.
A 60-W light bulb, a 120-W light bulb and a 240-W light bulb are connected
in series as shown in the figure. Which one of the following statements is
TRUE?
a)
b)
c)
d)
The 240-W light bulb is the brightest.
The 60-W light bulb is the brightest.
All three light bulbs glow with equal brightness.
The voltage drop is greatest across the 240-W light
bulb.
e) The voltage drop across all three light bulbs is the same.
10.
A current I =1 A flows around a plane circular loop of radius r=1 cm,
giving the loop a magnetic moment of magnitude m. The loop is placed in
⃗
a uniform magnetic field B=2
T with an angle φ=30 degrees between the
direction of the field lines and the magnetic dipole moment, as shown in
the figure. What is the magnitude of the torque τ on the current loop?
a)
b)
c)
d)
e)
τ
τ
τ
τ
τ
= 2π × 10−2 N-m
= π × 10−4 N-m
= 2π × 10−4 N-m
−2
=π
√× 10 N-m
= 3π × 10−4 N-m
11.
The circular loop in the figure is originally conducting current in a counterclockwise direction. The radius R of the loop is changed to R/2 and the
current is increased from I to 2I. Which of the following statements about
⃗ at the center of the loop is TRUE?
the magnetic field B
⃗ will increase by a factor of
a) B
2.
⃗ will increase by a factor of
b) B
4.
⃗ will decrease by a factor of
c) B
2.
⃗ will decrease by a factor of
d) B
4.
e) There will be no change in the
magnitude of the magnetic field
⃗ at the center of the loop.
B
12.
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?
a)
b)
c)
d)
e)
E
E
E
E
E
= 2.5 × 10−3
= 2.5 × 10−3
= 1.0 × 10−2
= 1.0 × 10−2
= 5.0 × 10−3
V/m;
V/m;
V/m;
V/m;
V/m;
counterclockwise.
clockwise.
counterclockwise.
clockwise.
counterclockwise.
13.
The circuit in the figure is connected to a 10-V battery. What is the current
I?
a)
b)
c)
d)
e)
14.
=2A
= 0.5 A
= 20 A
= 200 A
= 0.05 A
In the figure, you wish to apply a uniform magnetic field to the region
between the plates so that a particle with charge +q and velocity ⃗v = v0ˆı
will pass undeflected. The z-axis points out of the paper. Which is the
⃗ to apply?
correct magnetic field B
a)
b)
c)
d)
e)
15.
I
I
I
I
I
⃗
B
⃗
B
⃗
B
⃗
B
⃗
B
= (−E/(qv0 )) kˆ
= (−qE/v0 ) kˆ
= (−E/v0 ) ȷˆ
⃗ ˆı
= (q E)
= (E/v0 ) kˆ
y
E
+q
x
The figure shows, in cross section, several conductors that carry currents
through the plane of the figure. The currents have the magnitudes I1 =4 A,
I! 2 =5 A, and I3 =2 A, and the directions are shown. What is the line integral
⃗ clockwise around the path d shown in the figure? Note µ0 =
⃗ · dl
B
4π × 10−7 T ·m/A
a)
b)
c)
d)
e)
"
⃗
⃗ · dl=+44π
B
× 10−7 T ·m
⃗
⃗ · dl=+4π
B
× 10−7 T ·m
"
⃗ -4π × 10−7 T ·m
⃗ · dl=
B
"
⃗ -12π × 10−7 T ·m
⃗ · dl=
B
"
⃗ +12π × 10−7 T ·m
⃗ · dl=
B
"
16.
Which of the following statements is TRUE for ideal electronic instruments?
a) An ideal voltmeter has internal resistance Rin =0 and should be connected in parallel with the circuit element being measured.
b) An ideal voltmeter has internal resistance Rin =0 and should be connected in series with the circuit element being measured.
c) An ideal voltmeter has internal resistance Rin =infinity and should
be connected in series with the circuit element being measured.
d) An ideal ammeter has internal resistance Rin =0 and should be connected in series with the circuit element being measured.
e) An ideal ammeter has internal resistance Rin =infinity and should
be connected in series with the circuit element being measured.

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