Download Physics 1252 Exam #3E Instructions:

Physics 1252 Exam #3E
Thu, 21 April 2016
Name:
Physics 1252
Exam #3E
Instructions:
This is a closed-book, closed-notes exam. You are allowed to use a clean print-out of your
formula sheet, any scientific calculator, and a ruler. Do not write on your formula sheet,
except for your name: it must be handed in, signed but clean, with your exam.
There is space after each question to show your work; if you need more space, you may use
the back of the page, or request more paper. Please clearly indicate where your work for
each problem is. Underline or draw a box around your final answer.
The exam consists of four sections. Read all the questions at the start so that you can
allocate your time wisely. Do easy ones first!
You may not share your calculator. The use of cell phones or any other electronic devices (besides calculators) is prohibited. All such gadgets must be turned off and put away
throughout the exam.
• Do not open the exam until told to begin.
• You have the one entire class period to finish the exam.
• Put your last name on every page of the exam and on the formula sheet.
• You must provide explanations and/or show work legibly to receive full credit for
Sections II, III and IV.
• Make sure that your answers include appropriate units and significant digits. (Note:
For intermediate steps in your calculation, it’s best to carry more significant digits.)
• Fundamental constants and unit prefixes are on the Formula Sheet, last page.
By signing below, you indicate that you understand the instructions for this exam and agree
to abide by them. You also certify that you will personally uphold the university’s standards
of academic honesty for this exam, and will not tolerate any violations of these standards by
others. Unsigned exams will not be graded.
Signature:
UGACard #:
c 2016 University of Georgia. Unauthorized duplication or distribution prohibited.
Copyright Physics 1252 Exam #3E
Thu, 21 April 2016
Section
I
Score
Name:
II
/30
III
/35
IV (Bonus)
/35
/10
I: Multiple-Choice Questions (30 points)
For each question below, choose the single best response and write the corresponding
capital letter in the box provided. There is no penalty for guessing the wrong answer.
1. Two very thin circular rings, labeled 1 and 2 in the following, with radii R1 and R2 ,
respectively, and R1 > R2 , are both centered at the coordinate origin O ≡ (0, 0, 0), as
shown in the drawing.
Ring 1 lies in the x − y-plane with current I1 flowing around the ring in the direction
indicated in panel (B) of the drawing. Ring 2 lies in the z − y-plane with current I2
flowing around the ring in the direction indicated in panel (C) of the drawing.
Fig. 3.46
(A)
(B)
(C)
x
y
y
I1
1
2
z
I2
2
2
x
1
z
1
x
y
y
z
z-x-Plane View
z
x-y-Plane View
y
x
x
z
z-y-Plane View
Let B1 > 0 and B2 > 0 denote the magnetic field strengths produced at the origin O
~ ≡ (Bx , By , Bz )
by only I1 and only I2 , respectively. The total magnetic field vector B
produced by both currents at the origin O is then given by:
A.
B.
C.
D.
E.
(Bx , By , Bz ) = (0 , B1 − B2 , 0)
(Bx , By , Bz ) = (0 , B1 + B2 , 0)
(Bx , By , Bz ) = (−B2 , 0 , +B1 )
(Bx , By , Bz ) = (+B2 , 0 , −B1 )
(Bx , By , Bz ) = (−B2 , 0 , −B1 )
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Physics 1252 Exam #3E
Thu, 21 April 2016
Name:
2. A piece of straight wire carrying a current, I, is subjected to a uniform magnetic field,
~ Which one of the following figure panels could correctly represent the wire, its
B.
~
current flow direction, the B-field
direction and the direction of the magnetic force, F~ ,
exerted on the wire by the
magnetic field?
Fig. 3.51
F
I
I
I
B
B
(A)
A.
(B)
B.
I
(D)
(C)
C.
F
F
F
F
I
B
B
D.
B
(E)
E.
3. A molecular ion beam containing four different types of ions, called P , Q, R and S
here. The beam enters a uniform magnetic field, as shown in drawing below, with
~ perpendicular to, and pointing out of,
B 6= 0 above the lower horizontal line, and B
the plane of the drawing. The incident straight beam is in the plane of the drawing.
Fig. 3.15
B (out)
R
Q
P
S
B=0
~
The diameters of the semicircular ion trajectories in the B-field,
denoted by dP , dQ ,
dR and dS , respectively are observed to be in a ratio of
dP : dQ : dR : dS = 1 : 2 : 3 : 4 ,
as indicated in the drawing. Assume all four ion types carry the same absolute amount
~
of charge per ion, |q|, and they all enter the B-field
with the same kinetic energy K.
1
2
(Hint/Warning: K = 2 mv . Express v in terms of K !)
What is the ratio of the ion masses, denoted by mP , mQ , mR and mS , respectively ?
A.
B.
C.
D.
E.
mP
mP
mP
mP
mP
:
:
:
:
:
mQ
mQ
mQ
mQ
mQ
:
:
:
:
:
mR
mR
mR
mR
mR
:
:
:
:
:
c 2016 University of Georgia.
Copyright mS
mS
mS
mS
mS
= 11 : 12 : 13 : 41 .
= √11 : √12 : √13 : √14 .
= 1 : 4 : 9 : 16 .
= 1√ : 2 √
: 3 :√
4 . √
= 1 : 2 : 3 : 4 .
3
Physics 1252 Exam #3E
Thu, 21 April 2016
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4. A wire of some length L and with a circular cross-section of diameter D, made out of
a material with an electrical resistivity ρ, has a resistance of 250 kΩ. What will be the
resistance of a wire of length 15L and diameter 5D, made from a different material,
with a resistivity 2ρ?
A.
B.
C.
D.
E.
300 kΩ
75 kΩ
1500 kΩ
4500 kΩ
166.67 kΩ
5. Three different circuits, Z, Y and X, are built with the same three resistors, R1 ,
R2 , and R3 , and the same battery of battery voltage E, as shown in the drawing.
Compare and rank the magnitude of the voltage drops V1 across R1 , observed in the
three different circuits.
Fig. 3.33
Io
I3
I2
E
I1
Io
R3
R2
Io
R1
I2
E
R1
(Z)
A.
B.
C.
D.
E.
I1
I3
R3
(Y)
R2
I2
R2
I3
E
I1
R3
R1
(X)
V1 (Y ) < V1 (X) < V1 (Z)
V1 (Z) < V1 (X) < V1 (Y )
V1 (Z) < V1 (Y ) < V1 (X)
V1 (X) < V1 (Z) < V1 (Y )
V1 (X) < V1 (Y ) < V1 (Z)
6. In circuit Y in Fig.3.33, two of the resistances are R1 = 10 Ω and R2 = 20 Ω; and two
of the currents are I1 = 5A and I3 = 2A. What is the battery voltage E?
A.
B.
C.
D.
E.
10V
190V
90V
110V
200V
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Physics 1252 Exam #3E
Thu, 21 April 2016
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II: Circuit Analysis (35 points)
In the circuit shown below, assume that I1 = 2A, I4 = 4A, R1 = 7Ω, R2 = 6Ω, R3 = 8Ω,
C = 50 µF. Also assume that the capacitor is fully charged, by the voltage drop across it,
the left capactor plate carries a charge of Q = +200µF and there is no current flowing to or
from either capacitor plate.
Fig. 3.50
p
a
Io
I1
x
E
I3
q
I2
R1
IC
R3
C
RC
R2
y
I4
R4
b
(a) Find the electric potential difference, Vx −Vy , between check points x and y.
(b) Find the total current, Io . [Hint: Use a loop to find I2 , then a junction to find Io .]
(c) Find the battery voltage E. [Hint: Use a junction to find I3 , then a loop to find E.]
(d) How much heat is generated in resistor RC during 1 hour?
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Physics 1252 Exam #3E
Thu, 21 April 2016
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Work Space for Problem II:
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Physics 1252 Exam #3E
Thu, 21 April 2016
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III: Magnetic Fields and Forces (35 points)
Two very long thin straight wires running parallel to the z-axis and cutting through the
y-axis at y1 = 4m and through the x-axis at x2 = 5m, respectively, carry currents I1 and
I2 , both in the −z-direction, as shown in drawing below. I1 is 6 times as strong as I2 .
~ 1 and B
~ 2 , respectively, at point
The two currents produce magnetic field contributions B
P ≡ (5m, 4m, 0m) in the x − y-plane.
y
x-y-Plane View
Fig. 3.48
P
I1
y
z
I2
x
x
(a) What is the absolute value of the angle between the +x-direction and the total magnetic
~ =B
~1 + B
~ 2 , produced by the two currents at point P ? (Hint: You only
field vector, B
need the field strength ratio, B1 /B2 !)
~ = 3.2µT what are I1 and I2 ?
(b) If the total magnetic field strength at point P is B ≡ |B|
(c) Suppose an electron is shot through point P in the −z-direction with a speed of
3.6 × 105 m/s. Find the electron’s acceleration vector, ~a ≡ (ax , ay , az ) at P , due to
the magnetic force. State all three cartesian components of ~a. [Hint: Use the same
~ as found in (a) and given in (b), respectively.]
direction and strength of B
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Physics 1252 Exam #3E
Thu, 21 April 2016
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Work Space for Problem III:
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Physics 1252 Exam #3E
Thu, 21 April 2016
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IV: More Magnetic Force (10 points, Bonus)
Suppose the two current-carrying wires in Problem III are both 150m long, the current I2 is
7A and the ratio of the two currents is the same as given in Problem III. Find the magnetic
force F~ exerted by wire 1 on wire 2. State the strength of that force, F ≡ |F~ |, and the angle
between F~ and the +x-direction.
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