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Physics 1212 Exam #2A Instructions:

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Physics 1212 Exam #2A Instructions:
Physics 1212 Exam #2A
Thu, 19 March 2015
Name:
Physics 1212
Exam #2A
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 2015 University of Georgia. Unauthorized duplication or distribution prohibited.
Copyright Physics 1212 Exam #2A
Thu, 19 March 2015
Section
I
Score
Name:
II
/30
III
/35
/35
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. 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);
decrease if we increase d (keeping λ and L fixed);
increase if we decrease λ (keeping L and d fixed);
increase if we increase d (keeping λ and L fixed);
decrease if we increase L (keeping λ and d fixed).
2. If two point charges Q1 and Q2 at some distance r repel each other with a force of
10µN, 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 15µN
attract each other with a force of 13.33µN
attract each other with a force of 7.5µN
repel each other with a force of 15µN
repel each other with a force of 7.5µN
c 2015 University of Georgia.
Copyright 2
Physics 1212 Exam #2A
Thu, 19 March 2015
Name:
3. In a quadruple slit (4-slit) experiment‘ a 2nd order principal intensity maximum is
observed at an angle θ2 = 21.100o , measured from the central axis, and sin θ2 = 0.36.
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.
2
5
6
7
11
4. The figure below shows the volume, V, enclosed by an ellipsoidal surface, S, both
displayed by their intersections with the x-y-plane. Also shown are three point charges,
located in the x-y-plane as shown, with charge amounts Q1 = −4mC, Q2 = +7mC
~ present everywhere
and Q3 = −2mC. The three charges produce a net electric field, E,
inside, outside and on the surface of V. What is the net electrical flux, Φ, out of the
~ when multiplied by o ≡ 1/(4πk)?
surface S, due to this electrical field E,
Fig. 2.34
surface S
Q2
Q1
volume V
A.
B.
C.
D.
E.
Q3
o Φ = +1mC
o Φ = −6mC
o Φ = +3mC
o Φ = +11mC
o Φ = +5mC
c 2015 University of Georgia.
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Physics 1212 Exam #2A
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Name:
5. In the figure below, Q1 and Q2 are both negative point charges 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
Fig. 2.12
P
(D)
Q2
(E)
(C)
(A)
(B)
Q1
A.
B.
C.
D.
E.
6. A diffaction grating (in air or vacuum), is illuminated by coherent (laser) light with
wavelength λ and wave oscillation period τ = λ/c. The third 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 3 periods before A.
will arrive 4 periods before A.
will arrive 5/2 periods before A.
will arrive 3 periods before B.
c 2015 University of Georgia.
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Physics 1212 Exam #2A
Thu, 19 March 2015
c 2015 University of Georgia.
Copyright Name:
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Physics 1212 Exam #2A
Thu, 19 March 2015
Name:
II: 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, another maximum, at y1 = 3.920m, 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, a first order intensity
maximum is observed on the y-axis at y1 = 2.516m. 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 2015 University of Georgia.
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Thu, 19 March 2015
Name:
Drawing for Problem II (a):
c 2015 University of Georgia.
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Thu, 19 March 2015
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III: Electric Field from Point Charges (35 points)
Five point charges of unknown charge amounts, Q1 , Q2 , ..., Q5 , are positioned at various
unknown locations in the x-y-plane, excluding origin O ≡ (0, 0, 0). They jointly produce a
~ f ≡ [Ef,x , Ef,y , Ef,z ] with components Ef,x = +3N/C, Ef,y = −4N/C,
net electric field vector E
Ef,z = 0, at an observation point, P ≡ (xP , 0, 0) with xP = −5m, on the x-axis. The subscript
~ f is produced by the ”five” point charges.
”f” here is to remind you that E
A sixth point charge, Q6 = +25nC, is now added, placed at the origin, O, and all six point
~ = [Ex , Ey , Ez ].
charges, Q1 , Q2 , ..., Q6 , then jointly produce a net electric field, E
~ f with
(a) Draw this: big, on full blank page attached! Show: x-axis, y-axis, O, P , and E
~ 6 , produced by Q6 at P .
its tail end attached to P . Also show field contribution E
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 Q6 is removed again and an electron is placed, at rest, at point P and then released,
to accelerate subject to the electric field produced by the other five 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 2015 University of Georgia.
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Physics 1212 Exam #2A
Thu, 19 March 2015
Name:
Drawing for Problem III (a):
c 2015 University of Georgia.
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