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Physics 1252 Exam #2B Instructions:

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Physics 1252 Exam #2B Instructions:
Physics 1252 Exam #2B
Thu, 17 March 2016
Name:
Physics 1252
Exam #2B
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 and III.
• 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 #2B
Thu, 17 March 2016
Section
Score
I
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. In the figure below, Q1 is a negative and Q2 is a positive point charge with |Q1 | and |Q2 |
being of comparable magnitude. Which arrow drawn at P could correctly represent
~ generated by Q1 and Q2 at P ?
the electric field vector E
(C)
P
(D)
Q2
(E)
(A)
Fig. 2.30
(B)
Q1
A.
B.
C.
D.
E.
2. If two point charges Q1 and Q2 at some distance r repel each other with a force of
80µN, what force would they exert on each other if Q1 is tripled (×3) without change
of sign; r is quadrupled (×4), and the sign of Q2 is reversed ? The two charges will
A.
B.
C.
D.
E.
attract each other with a force of 60µN
attract each other with a force of 45µN
attract each other with a force of 15µN
repel each other with a force of 60µN
repel each other with a force of 15µN
c 2016 University of Georgia.
Copyright 2
Physics 1252 Exam #2B
Thu, 17 March 2016
Name:
3. A beam of coherent (laser) light of wavelength λ is incident upon a diffraction grating
with line spacing d, with λ < d, as shown in the figure below. Assume |∆y| is the
distance (in cm) between the two 1st-order intensity maxima, observed on a screen at
a distance L on the other side of the grating. This distance |∆y| will
1st order maxima
Fig. 2.03
Δy
Screen
θ
L
Diff. Grating
Laser Beam
A.
B.
C.
D.
E.
decrease if we increase λ (keeping L and d fixed);
increase if we increase d (keeping λ and L fixed);
increase if we decrease λ (keeping L and d fixed);
decrease if we increase d (keeping λ and L fixed);
decrease if we increase L (keeping λ and d fixed).
4. A positron is a sub-atomic particle with the same mass, but opposite charge as an
electron. If a positron is released, initially at rest, at a distance r from a spatially
fixed positive point charge, Q, the positron will accelerate to a final speed, v∞ , at a
very large (infinite) distance from the point charge. What would be the positron’s final
0
speed, v∞
, if instead it were released, initially at rest, at a distance r0 = 9r from a
positive point charge, Q0 = 11Q?
0
(A) v∞
=
0
(B) v∞
=
0
(C) v∞
=
0
(D) v∞ =
0
(E) v∞
=
121
v∞
81
√
11
v∞
3
√
11
v∞
9
√3 v∞
11
11
v∞
9
c 2016 University of Georgia.
Copyright 3
Physics 1252 Exam #2B
Thu, 17 March 2016
Name:
5. In a quintuple slit (5-slit) interference experiment, a 4th order principal intensity maximum is observed at an angle θ4 = 49.464o , measured from the central axis, and
sin θ4 = 0.76. How many principal maxima, total, including the central maximum, can
be observed across the entire, very wide (infinite-width) screen, i.e., between θ = −90o
and θ = +90o ?
A.
B.
C.
D.
E.
11
10
9
7
8
2
6. Two large, metallic, planar, parallel, charged capacitor plates have an electric potential
difference of V1 − V2 = +2500V, where V1 and V2 are the electric potentials on the top
and bottom plate, respectively, as shown here:
 Plate 1
Fig. 2.37
 Plate 2
An electron is shot through a small hole in the top plate, into the space between the
two plates. The electron, while traveling from the top to the bottom plate, ...
A.
B.
C.
D.
E.
will gain 4.0 × 10−16 J in kinetic energy between top and bottom plate.
will lose 2.0 × 10−16 J in kinetic energy between top and bottom plate.
will gain 2.0 × 10−16 J in kinetic energy between top and bottom plate.
will lose 8.0 × 10−16 J in kinetic energy between top and bottom plate.
must have a kinetic energy of at least 4.0 × 10−16 J, as it passes through the top
plate, in order to reach the bottom plate.
c 2016 University of Georgia.
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Physics 1252 Exam #2B
Thu, 17 March 2016
Name:
II: Electric Field from Point Charges (35 points)
Three point charges of unknown charge amounts, Q1 , Q2 , Q3 , are positioned at various un~o ≡
known locations in the x-y-plane. They jointly produce a net electric field vector E
[Eo,x , Eo,y , Eo,z ] with components Eo,x = +6.0N/C, Eo,y = −7.0N/C, Eo,z = 0, at an observation point, P ≡ (xP , 0, 0) with xP = +3m, on the x-axis.
A fourth point charge, Q4 = −24nC, is now added, placed on the x-axis at x4 = −1m and all
~ = [Ex , Ey , Ez ].
four point charges, Q1 , Q2 , Q3 , Q4 , then jointly produce a net electric field, E
~ o . Also
(a) Draw this: big, on full blank page attached! Show: x-axis, y-axis, Q4 , P , and E
~ 4 , produced by Q4 at P . Draw both E
~ o and E
~ 4 with their tail
show field contribution E
ends attached to P .
It does not have to be to scale, but all vectors must point into the correct quadrant or
along the correct coordinate axis direction.
~ at P ; its strength, |E|;
~ and its angle, θ, measured from
(b) Calculate the components of E
~
the +x-direction, with θ > 0 if E points above the x-axis, else θ < 0.
~ in the drawing from (a), as the resultant in a vector addition
Then also show E
parallelogram.
(c) Now Q4 is removed again and a muon is placed at point P and then released, to
accelerate subject to the electric field produced by the other three point charges. A
muon is a sub-atomic particle carrying the same charge as an electron, but with a mass
of 1.88 × 10−28 kg. Find the muon’s acceleration, ~a, immediately after its release at
P . State the magnitude of the acceleration, |~a|, and its angle, φ, measured from the
+x-direction, with φ > 0 if ~a points above the x-axis, else φ < 0.
Then also show ~a in the drawing from (a), correctly aligned with the relevant electric
field vector.
c 2016 University of Georgia.
Copyright 5
Physics 1252 Exam #2B
Thu, 17 March 2016
Name:
Drawing for Problem II (a):
c 2016 University of Georgia.
Copyright 6
Physics 1252 Exam #2B
Thu, 17 March 2016
Name:
III: Two-Source Interference (35 points)
Two small microwave sources, oscillating at the same frequency and in phase, are positioned
8m to the left of the y-axis, 3cm above and 3cm below the x-axis, respectively. A microwave
detector, P , moving up along the y-axis, observes a maximum in microwave intensity at
y0 = 0m, and, closest to that, an intensity minimum, at y1/2 = 3.640m, if the experiment
is performed in air, with an index of refraction nA = 1.000.
(a) Draw this: big, on full blank page attached! Show: x-, y-axes, detector, sources, line
connecting sources, observation angle θ, all given distances. It need not to be to scale.
Then find the oscillation frequency of the sources.
(b) How many intensity maxima, total, and how many intensity minima, total, will the
detector observe if it travels upward along the y-axis from very far below (y = −∞)
to very far above the x-axis (y = +∞)?
(c) If the entire experimental apparatus (sources, detector, and the entire space in between
sources and y-axis) is now submerged in a transparent liquid, the intensity minimum,
closest to the central maximum, is observed on the y-axis at y1/2 = 2.273m. What is
the index of refraction of this liquid for microwaves?
Hint: the frequency of the sources, the spacing between them, and their distance from
the y-axis is the same as before; but the speed of wave propagation is not.
c 2016 University of Georgia.
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Physics 1252 Exam #2B
Thu, 17 March 2016
Name:
Drawing for Problem III (a):
c 2016 University of Georgia.
Copyright 8
Physics 1252 Exam #2B
Thu, 17 March 2016
Name:
IV: Stopping the Muon (10 points, Bonus)
Suppose the muon in Part II(c) is shot directly at the spatially fixed point charge Q4 =
−24nC, with all other charges (Q1 , Q2 , Q3 ) having been removed. At a very large initial
distance (ri = ∞) from Q4 , the muon’s initial speed is vi = 14, 000m/s. How close to Q4 will
the muon get, before it stops? State this distance of closest approach, rf , in units of meters.
Hint: To ”stop” means: having a speed vf = 0!
c 2016 University of Georgia.
Copyright 9
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