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Physics 1252 Exam #2E Instructions:

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Physics 1252 Exam #2E Instructions:
Physics 1252 Exam #2E
Thu, 17 March 2016
Name:
Physics 1252
Exam #2E
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 #2E
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. If two point charges Q1 and Q2 at some distance r repel each other with a force of
20µN, what force would they exert on each other if Q1 is tripled (×3) without change
of sign; r is doubled (×2), and the sign of Q2 is reversed ? The two charges will
A.
B.
C.
D.
E.
attract each other with a force of 30µN
repel each other with a force of 15µN
repel each other with a force of 30µN
attract each other with a force of 26.67µN
attract each other with a force of 15µN
2. In the figure below, Q1 is a negative and Q2 is a positive point charge. Which arrow
~ generated by Q1 and
drawn at P could correctly represent the electric field vector E
Q2 at P ?
(C)
P
(D)
Q2
(E)
(A)
Fig. 2.30
(B)
Q1
A.
B.
C.
D.
c 2016 University of Georgia.
Copyright E.
2
Physics 1252 Exam #2E
Thu, 17 March 2016
Name:
3. In a quadruple slit (4-slit) interference experiment, a 3rd order principal intensity maximum is observed at an angle θ3 = 43.630o , measured from the central axis, and
sin θ3 = 0.69. 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.
13
12
11
9
10
4. A muon is a sub-atomic particle with the same charge as an electron. If a muon is
released, initially at rest, at a distance r from a spatially fixed negative point charge,
Q, the muon will accelerate to a final speed, v∞ , at a very large (infinite) distance
0
, if instead it were
from the point charge. What would be the muon’s final speed, v∞
released, initially at rest, at a distance r0 = 4r from a negative point charge, Q0 = 7Q?
0
=
A. v∞
B.
C.
D.
E.
0
v∞
0
v∞
0
v∞
0
v∞
=
=
=
=
√
7
v∞
2
√
7
v∞
4
49
v
16 ∞
7
v
4 ∞
2
√ v∞
7
c 2016 University of Georgia.
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Physics 1252 Exam #2E
Thu, 17 March 2016
Name:
2
5. Two large, metallic, planar, parallel, charged capacitor plates have an electric potential
difference of V1 − V2 = +7500V, where V1 and V2 are the electric potentials on the top
and bottom plate, respectively, as shown here:
 Plate 1
Fig. 2.36
 Plate 2
An electron is shot through a small hole in the bottom plate, into the space between
the two plates. The electron, while traveling from the bottom to the top plate, ...
A. will gain 12.0 × 10−16 J in kinetic energy between bottom and top plate.
B. must have a kinetic energy of at least 12.0 × 10−16 J, as it passes through the
bottom plate, in order to reach the top plate.
C. will gain 6.0 × 10−16 J in kinetic energy between bottom and top plate.
D. will gain 24.0 × 10−16 J in kinetic energy between bottom and top plate.
E. will lose 12.0 × 10−16 J in kinetic energy between bottom and top plate.
6. A diffraction grating (in air or vacuum), is illuminated by coherent (laser) light with
wavelength λ and wave oscillation period τ = λ/c. The 5th order intensity maximum,
to the right of the central intensity maximum M , is located at point Q, as shown in the
figure below. A wave crest A, from slit R, and a wave crest B, from the neighboring
slit S to the right of R, have departed at the same time from their respective slits of
origin. Therefore, at Q,
M
Q
Fig. 2.29
R S
Diffr. Grating
Laser Beam
A.
B.
C.
D.
E.
A
B
B
B
A
and B will arrive at the same time.
will arrive 6 periods before A.
will arrive 9/2 periods before A.
will arrive 5 periods before A.
will arrive 5 periods before B.
c 2016 University of Georgia.
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Physics 1252 Exam #2E
Thu, 17 March 2016
Name:
II: Two-Source Interference (35 points)
Two small microwave sources, oscillating at the same frequency and in phase, are positioned
7m below the x-axis, 2cm to the left and 2cm to the right of the y-axis, respectively. A
microwave detector, P , moving along the x-axis, observes a maximum in microwave intensity
at x0 = 0m, and, closest to that, an intensity minimum, at x1/2 = 1.127m, 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 along the x-axis from very far to the left (x = −∞) to
very far to the right (x = +∞)?
(c) If the entire experimental apparatus (sources, detector, and the entire space in between
sources and x-axis) is now submerged in a transparent liquid the intensity minimum,
closest to the central maximum, is now observed on the x-axis at x1/2 = 0.983m. 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 x-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 #2E
Thu, 17 March 2016
Name:
Drawing for Problem II (a):
c 2016 University of Georgia.
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III: Electric Field from Point Charges (35 points)
Four point charges of unknown charge amounts, Q1 , Q2 , Q3 , Q4 , are positioned at various unknown locations in the x-y-plane. They jointly produce a net electric field vector
~ o ≡ [Eo,x , Eo,y , Eo,z ] with components Eo,x = +6.5N/C, Eo,y = −3.5N/C, Eo,z = 0, at an
E
observation point, P ≡ (xP , 0, 0) with xP = −3m, on the x-axis.
A fifth point charge, Q5 = +25nC, is now added on the x-axis at x5 = +2m and all five
~ = [Ex , Ey , Ez ].
point charges, Q1 , Q2 , Q3 , Q4 , Q5 , then jointly produce a net electric field, E
~ o . Also
(a) Draw this: big, on full blank page attached! Show: x-axis, y-axis, Q5 , P , and E
~ 5 , produced by Q5 at P . Draw both E
~ o and E
~ 5 with their
show the field contribution E
tail 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
~ points above the x-axis, else θ < 0.
the +x-direction, with θ > 0 if E
~ in the drawing from (a), as the resultant in a vector addition
Then also show E
parallelogram.
(c) Now Q5 is removed again and an electron is placed at point P and then released, to
accelerate subject to the electric field produced by the other four point charges. Find
the electron’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.
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Physics 1252 Exam #2E
Thu, 17 March 2016
Name:
Drawing for Problem III (a):
c 2016 University of Georgia.
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Physics 1252 Exam #2E
Thu, 17 March 2016
Name:
IV: Speeding Up the Electron (10 points, Bonus)
Suppose the electron in Part III(c) is shot directly at the spatially fixed point charge Q5 =
+25nC, with all other charges (Q1 , Q2 , Q3 , Q4 ) having been removed. At a very large initial
distance (ri = ∞) from Q5 , the electron’s initial speed is very small, vi ∼
= 0m/s. How close to
Q5 must the electron get in order to reach a speed of vf = 600, 000m/s? State this distance,
rf , in units of meters.
c 2016 University of Georgia.
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