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Unformatted text preview: Physies M see Erna}; Exam Name Seetion: Part l: ghort Answer (4pm each) Circle the best answer: 1) A bar of copper (good conductor) has a cubic cavity centered in the casting that
contains a charge q (not touching the conductor). The net charge on the conducting
bar is —2 mC and the charge Q on the outer surface of the bar is 1 inc The charge (1
is: a) ——2 mC.
b) +3 mC.
c) ~3 mC
d) +2 mC. 2)
I An increasing current I flows in a straight wire. The flow of induced current a) is clockwise for loop 1 and counterclockwise for loop 2. b) is counterclockwise for loop 1 and counterclockwise for loop 2.
c) is clockwise for loop 1 and clockwise for loop 2. d) is counterclockwise for loop 1 and clockwise for loop 2. 3) Four identical bulbs are connected as shown. Which is the dimmest? a) a and c are equally bright and dimmer than the others.
b) b is dimmer than the others. 0) d is dimmer than the others.
d) The bulbs are all equally bright. E. E 4:) At a given place and time the E~ﬁeld of a light wave is in the +2 direction and its B
ﬁeld is in the +x direction. a) The wave propagates in the =y—direction.
b) The E and B fields have the same amplitude.
c) A possible expression for the E—ﬁeld is E 2 E0 003(k)) .— mt) d) If a polarizer with transmission axis in the z—direction is placed in the path of
the wave, the wave’s energy will be absorbed by the ﬁlter. 5) A: The E—ﬁeld produced by the sphere shown is measured at distance 2R and at distance R/4
from the center, and at both points the ﬁeld has magnitude E0 and is directed toward the center. Which of the following is NOT true? (a)
(b)
(C)
(d) The net charge carried by the sphere is negative.
At the center the field is zero. The sphere is a conductor. At the surface of the sphere the field has magnitude 4E0. 6) Two wires carry unequal currents in opposite directions. A charge Q is placed in
between them inside an uncharged nonconducting box as shown. a)
b)
C)
d) The net magnetic flux out of the volume is nonzero, while the net electric ﬂux
is zero. The net magnetic flux and the net electric flux out of the volume are both
zero. The net electric flux out of the volume is not zero, while the net magnetic
flux is zero. The net magnetic ﬂux and net electric ﬂux out of the volume are both
nonzero. 7) An object: (arrow) is placed near a lens with a positive focal length f as shown. The
image is a) real and larger than the object. b) real and smaller than the object. c) virtual and larger than the object.
d) virtual and smaller than the object. 8) The power dissipated in the top resistor on the upper right is. a) 1/6IZR
b) 1/9 12R
0) 1/3 12R
d) 4/9 12 R. 9) Two positive charges are fixed in space on the x—axis. Both the electric ﬁeld and the
electric potential are zero very far away from the charges. a) Both the net electric field and the electric potential can be zero somewhere in
between the charges. b) Neither the net electric ﬁeld nor the electric potential can be zero in between
the charges. c) The net electric ﬁeld can be zero somewhere in between the charges, but the
electric potential is nonzero except far away from both charges. (1) The net electric field at points oﬂ of the x—axis is always along the x—axis. 10) Two batteries are connected to a resistor R as shown. What value of R produces a
current I of 2 A? 21) 8Q
b) 69
c) 49
d) 20 wig g: ll) A transformer has 100 turns in the primary (input) winding and 200 turns in the secondary (output) winding that is connected to a load (not shown). The primary is
connected to a battery, producing a constant current. a) The current in the secondary is larger than the primary.
b) The voltage in the secondary is larger than the primary.
c) The voltage and current in the secondary are both 0. d) The output power equals the input power. 12) Along thin copper tube carries a current I out of the page (shaded). Along copper
wire (7:) in the center of the tube carries a current 1 into the page. Let Bl be the ﬁeld
at P1 and 32 be the ﬁeld at P2. Which of the following is correct? a) BI is nonzero and in the y direction; B; is zero. b) Bl is non—zero and in the x direction; 82 is zero. c) 31 is non—zero and in the X direction; 32 is non—zero and in the X direction.
(1) B} is zero; 32 is non—zero and in the y direction. 6) B1 is nonuzero and in the y direction; 32 is non—zero and in the y direction. 13) Light with a wavelength hair in air passes through a coating of thickness t and index
of refraction n = 2 and then reﬂects from a conductor (hatched). What is the minimum
nonzero thickness t that has a maximum reflection? a) hat, /8
b) hair/4
G) 7mm /2
d) Q\lair 14) Monochromatic light illuminates two slits at an angle (b as shown. The intensity is
zero on a screen at point P, which is located along the centerline of the slits. The vertical
positions of the ﬁrst few maxima and minima are observed at small angles with respect to
the horizontal axis. The ratio of the vertical positions of the second and first maxima, yz/yl, is: a) 2:1
b) 3:1
0) 4:1
d) 5:1 _—:j_ Ht art sci 4—H
l I *r‘ I In t 15) A 1.5 farad and a 0.5 farad capacitor are connected to a 10 V battery (left) and ﬁilly
charged. A pair of l farad capacitors are connected to a different battery (right). For what
voltage V2 is the total stored energy the same in both circuits? a) 5 V.
b) 10 V.
c) 20 V.
d) 40 V. 0" 30° 90°
1 :> 1 3 2 16) Two polarizing sheets 1 and 2 are placed together with their transmission axes
crossed so that no light is transmitted. A third sheet is inserted between them with its transmission axis at an angle of 30° with respect to that of the ﬁrst sheet. If
zmpolarz‘zed light of intensity I is normally incident on the ﬁrst polarizing sheet, then
the transmitted intensity through the threesheet combination is: (Use 00330 = sqrt(3/4), c0560 = 1/2 and cos90 = O)
a) 0 b) 1/2 I c) 3/8 I d) 3/32 I e) 1/16 I 17) An electromagnetic wave with hair = 0.6 mm is transmitted through two 12 mm
thick dielectric plates with different indices of refraction. Assuming the light is in~phase when it enters the plates, the phase difference (1)1 — (1)2 when the light emerges is a) 57:.
b) 1071:. c) 20 7c.
(1) zero. 18) A negative charge is placed in a uniform electric field. Points 2 and l are separated
by a distance d. a) The electric potential at 1 is higher than at 2 and the potential energy of the
charge is lower. b) The electric potential at 1 is lower than at 2 and the potential energy of the
charge is higher. c) The electric potential at 1 is higher than at 2 and the potential energy of the
charge is higher. (:1) The electric potential at 1 is lower than at 2 and the potential energy of the
charge is lower. 19) A negativebz charged particle moves at a speed v in the direction of the arrow in a
uniform magnetic ﬁeld into the page. The direction of the force vector acting on the charge is in quadrant a) 1.
b) 2.
c) 3.
d) 4. 20) I stand in air and View a lead sphere that is suspended in the water. Two possible rays
are shown (dashed line is normal to the surface). The sphere appears a) closer to the surface of the water than it actually is.
b) further down in the water than it actually is.
c) at the same depth as it actually is. 21) A long solenoid (shown in cross section) produces a B—ﬁeld into the page as
shown in the shaded region (x)’s , which is increasing with time at a
constant rate. (Assume the field outside the solenoid is negligibly small, so
that ﬂux arises only from the ﬁeld in the solenoid.) A circuit with two light
bulbs surrounds the solenoid. When the switch is closed: (a) Bulb B goes out and the brightness of bulb A does not change.
(b) Bulb B goes out and bulb A gets brighter. (c) Both bulbs go out. (d) Nothing changes. 22) Maxwell’s equations imply all of the following EXCEPT:
(a) A magnetic ﬁeld must exist between the plates of a discharging capacitor. (b) If a volume of space contains net positive charge, more electric flux enters the
volume than leaves it. (c) The ﬁelds in an electromagnetic plane wave must obey the relation E = CB.
((1) Magnetic field lines never begin or end. (e) A changing magnetic ﬁeld can cause an electric current to flow. 23) An induced current is produced in a circular loop of wire when:
(a) The loop remains at rest in a static, non—uniform magnetic ﬁeld.
(b) The loop remains at rest in a static, uniform magnetic ﬁeld.
(c) The loop moves at constant velocity in a static, nonuniform magnetic ﬁeld. (d) The loop moves at constant velocity in a static, uniform magnetic ﬁeld. 24) Light bounces inside a ﬁber with an index of refraction n = 2. Air is outside the fiber.
What is the smallest value of 9 for which the light is totally internally reﬂected? a) 90°.
b) 60°.
c) 30°.
d) 0°. 25) Oscillating electric and magnetic ﬁelds at a point in space are given at time t = O by R
= E (4 j + 3 lt)/5 and the magnetic ﬁeld is B = (E/c) (3 j  4 lag/5, with E the ﬁeld
magnitude. Can this be an electromagnetic wave propagating in a vacuum? if so, What is
its direction of propagation? a) Yes, since E and B are perpendicular. The wave would propagate along i.
b) Yes, since E and :8 are perpendicular. The wave would propagate along  i.
c) No. d) Yes, since EXE :1: O. The wave would propagate along i. Pent ii: Leng Answet % ®®®®®
®®®®® l) (ZOpts) A square loop with a side of length L = 2 m is placed with halfof its area in a uniform magnetic ﬁeld B of 3 T into the page. The loop has a resistance of 5 Q. Use
00345 = sin 45=1/sqrt(2). a) if B is increasing in magnitude at a rate of 5 T/sec, What is the total induced
EMF 8 in the loop, what is the current in the loop and which way is it ﬂowing
(CW or COW)? b) Find the X— and y—components of the total force on the loop. Q1 Q2 A A
E}% WEQ WE Cit 012 Q3 Q4 2) (20 pts) Two large conducting plates are separated by a distance that is small
compared to their size. The electric ﬁelds are shown as arrows perpendicular to the
large surface of each plate, which is A = 2 tn2 for each side. The charge on each
surface is denoted q}, (12, C13, C14. Suppose the total charge q1+ (12 on the left plate is Q1
= 27 2C ( 1 pC : 10‘12 C), 31 = 2 MC, and :33 = 4 N/C. For this problem, take 80 = 9
x 10' . a) Find q}.
b) Find E2.
c) Find (13. (1) Find the total charge Q2. 3) (20 pts) A resistor R of length L sits in a uniform electric field E polarized along it 60 and a uniform magnetic field B polarized perpendicular to it. A circuit
permits current to flow. For the given electric ﬁeld, find the voltage across the resistor and the
power dissipated in the resistor in terms of L, R, and E. Find the magnitude and direction of the magnetic force on the resistor, in
terms of d, L, R, and B. (Assume the current in the resistor ﬂows in a
straight line.) Suppose that E and B arise from an electromagnetic wave. Show explicitly
that the ratio of the (instantaneous) power dissipated in the resistor to the
magnitude of the magnetic force on the resistor is just the speed of light,
0. (Ignore the wires in the circuit, assuming the light beam is focused on
the resistor only.) What does the answer to part (c) this tell you about the ratio of the energy
absorbed from the light by the resistor to the momentum imparted to it? remnants: “ﬂy1
—‘%lﬂ=t
Ht”? 126ml I l 4) (20 pts) Optics.
A) A nearsighted person has a near point frOm the eye of 15 cm and a far point of 1.5 m. a) Find the focal length of a corrective contact lens placed on the eye that makes it
possible to see objects clearly when they are very far away. b) With the contact lens of part (a) on, what is the new near point? c) Suppose that with the contact lenses on, you put on someone’s reading glasses
(placed 2 cm from your eye). You find that you can read a book no closer than 25
cm from your eye. Using the result of part (b), find the focal length of the reading
glasses. Jupiter is about 0.6 billion kilometers (360 million miles) from earth and has 12
moons. One moon, called lo, is r = 400 thousand kilometers from the center. Assume
the observed light from Jupiter has an average wavelength of 600 nm. Use the small angle approximation, sine = tanG : 9. a) Is 10 resolvable with a telescope that has an aperture of 5 cm? Screen 5) (20 pts) Two sources radiate light of wavelength A in all directions, with a polarization
out of the page. The sources are separated by a distance equal to twice the wavelength.
The interference pattern of the light is observed on a screen that is far away compared to
the wavelength, so that the paths are nearly parallel as shown. a. Find the dzﬁerence between the path lengths from the two sources
to the screen in terms of h and 9 for any value of 9. b. If the sources have the same phase, ﬁnd all of the angles 8 from O
to 90° such that a maximum intensity is observed. c. Now suppose that the sources are out of phase by 180°. Again ﬁnd
all of the angles 8 from O to 90° such that a maximum intensity is
observed. ...
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 Spring '09
 Thomas
 Physics

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