Download Solutions to Practice Exam #3

Physics 111
Second Hour Exam
February 13, 2006
Name___________________________
Multiple Choice
/20
Problem 1
/26
Problem 2
/25
Problem 3
/29
------------------------------Total
/100
Part I: Multiple-Choice
Circle your answer to each question. Any other marks will not be given credit.
Each multiple-choice question is worth 2 points for a total of 20 points.
1. The dead-quiet “caterpillar drive” for submarines as seen in the movie The Hunt
for Red October is based on a magnetohydrodynamics (MHD) drive. As the ship
moves forward, seawater flows through multiple channels (one of which is shown
below) in a structure built around the rear of the hull. Magnets (shown but not
labeled) are positioned along opposite sides of the channel with opposite poles
facing each other; create a magnetic field within the channel. Electrodes create an
electric field across the channel as shown. The electrodes drive a current across
the channel and through the water, the magnetic field propels the water toward the
rear of the channel creating a propulsion system. What direction should the
magnetic field be oriented so the water is propelled out the back of the channel?
a. upward
b. downward
c. to the right
d. to the left
2. A current of 17mA is maintained in a single circular loop with a circumference of
2m. A magnetic field of 0.8T is directed parallel to the plane of the loop. The
magnitude of the torque on the loop is due to the magnetic field is
a.
b.
c.
d.
zero
0.004 Nm
0.014 Nm
0.027 Nm
3. In vacuum, the speed of light depends on
a.
b.
c.
d.
the frequency of light.
the wavelength of light.
all of the above.
none of the above.
4. A long-straight current carrying wire that has 6 A of current passes through the
center of a circular coil of wire of radius 5cm. The wire is perpendicular to the
plane of the coil. If the current in the wire increases at a rate of 1 A/s, the induced
current generated in the coil is
a.
b.
c.
d.
6A clockwise for a 1 resistance coil.
6A counterclockwise for a 1 resistance coil.
zero.
unable to be determined since the direction of the current in the wire is
unknown.
5. Two conducting loops face each other a distance d apart. An observer sights
along their common axis from left to right. If a clockwise current is suddenly
established in the larger loop by a battery not show, the direction of the induced
current in the smaller loop is
a.
b.
c.
d.
zero.
clockwise
counterclockwise
unable to be determined since the magnitude of i is unknown.
6. A Boeing KC-135A refueling airplane has a wingspan of 39.9m and flies at a
constant altitude in a northerly direction with a speed of 850 km/hr. If the vertical
component of the Earth’s magnetic field is 5.0x10-6 T, what is the induced emf
between the wing’s tips?
a.
b.
c.
d.
0 mV
21 mV
47 mV
170 mV
7. Your eye sees in a typical wavelength range of 400nm – 700nm. A typical
medical x-ray has a wavelength of approximately
a. 800 nm
b. 300 nm
c. 1x109 nm
d. 0.1 nm
8. A microwave oven is powered by an electron tube called a magnetron, which
generates microwaves with a frequency of 2.45 GHz. (Giga stands for a billion.)
The microwaves enter the oven and are reflected by the walls. The standing-wave
pattern produced in the oven can cook food unevenly with hot spots in the food at
antinodes and cool spots at the nodes, so a turntable is often used to rotate the
food and distribute the energy. If a microwave oven intended for use with a
turntable is instead used with a cooking dish in a fixed position, the antinodes
appear as burn marks on the food. If the separation distance between the burns is
measured to be 6cm, what is the speed of the microwaves?
a. 3x108 m/s
b. 1.5x108 m/s
c.1.5x1010 m/s
d.2.5x10-11 m/s
9. A plane flies at constant speed due north through the Earth’s magnetic field that
has components that point both north and vertically down. In this situation,
a.
b.
c.
d.
the left side of the plane becomes positively charged.
the right side of the plane becomes positively charged.
the top of the plane becomes positively charged.
the bottom of the plane becomes positively charged.
10. A wooden ring is dropped vertically through a region of space containing a
magnetic field, shown below right. Due to electromagnetic induction only the
direction of the current in the ring is
A
a.
b.
c.
d.
clockwise.
counterclockwise.
alternating both clockwise and counterclockwise.
zero.
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
B
Part II: Free Response Problems
Please show all work in order to receive partial credit. If your solutions are
illegible no credit will be given. Please use the back of the page if necessary, but number
the problem you are working on. The numbers in parentheses following the question
correspond to the point values for each part.
1. The solar wind is a steam of charged particles, mainly protons and electrons that are
ejected from the Sun and travel outwards through space. When the solar wind
encounters the magnetic field of the Earth the charged particles spiral down the
magnetic field lines near the poles and excites atoms in the atmosphere causing the
aurora. Suppose that the protons and the electrons in the solar wind are traveling with
a velocity of 6.5x106 m/s. and enter the Earth’s magnetic field (5.5x10-5 T directed
straight down at the North Pole) at an angle of 65.5o with respect to the field.
a. Starting with F = ma, derive an expression for the period of the circular orbit for
any charged particle. (Hint: The period is the time it takes the charged particle to
make one complete trip the circular loop.) (8)
FB  FC  qv B 
T 
mv2
qBR
2R

 v 
R
m
T
2m
qB
b. What is the period of the electron’s orbit? Of the proton’s orbit? (6)
2 1.67 10 27 kg

1.6 10 19 C  5.5 10-5 T
2  9.1110 31 kg
Te 

1.6 10 19 C  5.5 10-5 T
Tp 
c.
The resultant motion of the charged particles is a helix around the magnetic
field lines. Derive an expression for the pitch of the helix, where the pitch is
defined as the distance the particle travels parallel to the magnetic field in one
revolution about the magnetic field line. (6)
p  vllT  v cos T
d.
What is the pitch of the electron’s orbit? Of the proton’s orbit? (6)
pe  6.5 106 ms   cos 65.5 
p p  6.5 106 ms   cos 65.5 
2. A light bulb in a circuit, shown below in the sketch, has a resistance of 12 and
consumes 5W of power where a 1.25m long rod moves to the right with a constant
speed of 3.1 m/s.
a. What is the magnetic field that will produce these results above? (8)
P  I 2R 
BLv 2
R
B
PR

L2 v 2
5W  12
1.25m 2 3.1 ms 2
 2.0T out of the page.
b. What external force is needed to pull the rod to the right at this speed? (6)
B 2 L2 v 2T  1.25m  3.1 ms 
Fext  FB  ILB 

 1.61N to the right.
R
12
2
2
c. What is the magnitude and direction of the current that flows in the circuit? (6)
BLv 2T 1.25m3.1 ms 

0.65 A  650mA counterclockwise to oppose the
R
R
12
increase in magnetic flux.
I


d. Does all of the mechanical work done by the external force get transformed to
thermal energy in the wire? (5)
At first glance, the answer should be yes since the mechanical work per unit time
the external force does is converted to electrical energy per unit time which is
converted to thermal energy in the wire and the wire heats up. However, not only
does the wire heat up as heat is dissipated by the conversion of electrical energy
to thermal energy, but a small amount of this energy is also transformed in to light
since the charges in the wire are accelerated by the induced electric field and the
external magnetic field.
3. Rail guns have been suggested for launching projectiles into space without the need
for chemical rockets, and for ground to air antimissile weapons of war. A crude
tabletop (hand-held) model is shown below. When the trigger is squeezed closed
current flows in the circuit and the 500-mg projectiles are fired off of the ends of the
rails at the target.
100cm
Trigger
3.5cm
a. What is the magnetic field created at the midpoint of the bar if a 60-A current
flows through the circuit? (Hint: Assume that the field at the midpoint is due
only to magnetic fields created by currents flowing in the top and bottom rails,
which can be modeled as two long straight wires.) (8)
I
60 A
Bnet  Bupper  Blower  2 0  4 10 7 TmA
 0.00137T  1.37mT
2r
0.0175m
into the page
b. What are the magnetic force and corresponding acceleration of the bar? (8)
F  ILB  60 A  0.035m  0.00137T  0.0029 N  2.9mN
F
0.0029 N
a 
 5.76 sm2
m 500 106 kg
both to the right.
c. If the projectiles are accelerated from rest over a distance of 1 meter, with what
velocity (in m/s and mi/hr) do the projectiles leave the rails? (6)
2 Fx
20.0029 N 1m 
W  Fx  12 mv2  v 

3.4 ms  7.36 mi
hr to the right.
m
500 10 6 kg
d. Suppose that the speed in part c is too small for your liking. Suppose that you
would like the projectiles to leave the rails at 850 miles per hour (about 394 m/s),
what current would you need to produce this speed? (Notes: The smallest
working models of theses have been developed by the Navy and are being tested
on battleships. Also for a great rendition of a tabletop model, watch the movie
Eraser with Arnold Schwarzenegger.) (7)
W  Fx  12 mv 2  F 
mv 2
 2 I 
 ILB  IL 0  
2x
 2r 
  500  10 6 kg  394 ms   0.0175m
mrv 2

 6965 A
2x 0 L
2  1m  0.035  4  10 7 TmA
2
I
Physics 111 Equation List
q1q2
rˆ
r2

 F
E
q*
PE = -B cos
F k
E
q
4 o r 2

n
Ceq   Ci caps in parallel 
i 1
rˆ
o I

2 r
n
1
1

caps in series 
Ceq i 1 Ci


 B  BA cos  

induced=BLv

Prad 
B
 B

t
PE (r ) 
q1q2
4 0 r
 induced   N
V (r ) 
q
PE
B2
S
Prad 

 12  o E 2  12
c
Volume
o
PE
Energy
S c

E  cB
Volume time  Area
c 2
c 2
I  S  0 Emax

Bmax  = B sin
2
20
4 o r
V
Ex  
x
Q  CV
Co 
o A
d
parallel-plate cap
PE  12 QV  12 CV 2  12
Q2
C
PE 1
 2 oE2
V
C  Co
Q
I
t
L
R
A
PEE
V2
P
 IV  I 2 R 
t
R
V  IR
S t  S 0 cos 2 
E=hf
p=h/
c=f
ir
n1sin1 = n2sin2
sin c = n2/n1
n = c/v
n
1
1
  R' s in parallel
Req i 1 Ri
n
Req   Ri R' s in series
i 1

2S

c
Constants
1
k
 9 x109 Nm2 / C 2
4 o
Constants
o  4 107 Tm / A
g = 9.8 m/s2
c = 3 x 108 m/s
h = 6.63 x 10-34 Js
0 = 8.85x10-12 C2/Nm2
me = 9.11x10-31 kg
mn = 1.69x10-27 kg
mp = 1.67x10-27kg
31.6x106s = 1yr
t
Q  Qo e RC
FM = qvB sin
FM = ILB
IA

