Final Exam
PHY 2140
Row:
Seat:
Date, 2003
Please type your name here
Please type your student number here
Instructions:
The following procedure must be followed in order to correct any (unlikely) mistakes in
the grading.
1. Do all the questions. Show your work to receive credit. I must be able to
understand what you have done while I am reading the exam – not when you
explain it to me after the exam is graded and returned.
2. For each problem:
(a) write down any formula(s) used
(b) justify why you used that particular formula(s)
(c) copy the answer you have circled from the exam pages
to the General Purpose Answer Sheet and fill in the ovals.
(d) show your work! No work – no point.
3. The formula sheet is on the last page of the exam. You may detach it from the rest
of the exam.
I have read and understood the statement above
Your signature
NAME
1.
Determine the point nearest the charges where the total electric field is zero. Take the 6.00 C
charge to be at the origin of the x axis.
22..0000 m
m
a.
b.
c.
d.
e.
2.
–1.80 m
–1.15 m
0.41 m
0.78 m
1.15 m
66..0000 C
C
1155..00 C
C
Find the charge on the 3 F capacitor in the following circuit.
a.
b.
c.
d.
e.
44 FF
33 FF
20 C
24 C
28 C
32 C
not enough information
66 FF
1122 V
V
3.
Two identical parallel conducting plates of area 0.25 m2 are placed with their centers 0.0030 m
apart. Initially, the first plate has a charge of 12 x 10 -9 C and the second a charge of -18 x10-9 C.
The plates are then connected by a conducting wire. Find the potential difference between the two
plates when the charges are in equilibrium. (Hint: first find the capacitance of the two plates.)
a.
b.
c.
d.
e.
4.
–4.1 V
–8.1 V
–13 V
–16 V
not enough information
What is the current through the 2.00  resistor?
a.
b.
c.
d.
e.
0.125 A
0.250 A
0.375 A
0.500 A
0.625 A
11 

22 

11 

1155 

1122 V
V
5.
A cube with an edge of length l = 0.04 m is placed in a uniform magnetic field throughout the
region that has components Bx = 0, By = 4 T and Bz = 3 T. Find the net flux through the cube.
a.
b.
c.
d.
e.
zz
Zero
0.0064 Tm2
0.0048 Tm2
0.12 Tm2
0.16 Tm2
xx
yy
6.
Two long straight wires 0.004 m apart carry currents of 5.0 A and 10 A as shown. Find the net
magnetic field midway between the wires. Take B as positive if it is going into the page.
a.
b.
c.
d.
e.
–5.0 x 10-4 T
5.0 x 10-4 T
–1.0 x 10-3 T
1.0 x 10-3 T
Zero
1100 A
A
55..00 A
A
00..00004400 m
m
7.
As part of his stage show, Ozzie Osbourne constructs a “guillotine” consisting of a metal blade of
length 1.50 m and mass 0.50 kg that can slide without friction along rails. To slow down the metal
blade, the rails are placed in a 2.00 T magnetic field and can carry current. Find the velocity of the
blade, assuming that there is no net force on the bar and that the resistance R = 1.00 . Hint: the
current through the resistor depends on the velocity of the blade.
RR
a. 0.54 m/s
b. 0.76 m/s
BB
c. 1.25 m/s
I
d. 4.79 m/s
e. At long last, the Prince of Darkness
meets the Prince of Darkness.
vv
11..5500 m
m
8.
After the concert, Kid Rock presents a golden neck brace to his hero Ozzie Osbourne. To impress
him, he spins the brace about a vertical axis at a frequency of 60 Hz in a magnetic field of B = 0.5
T as shown. If the area of the brace is 5.0 x 10 -3 m2, calculate the maximum emf induced in the
brace.
a.
b.
c.
d.
e.
9.
0.76 V
0.94 V
1.18 V
1.27 V
none of the above
If the kinetic energy of a rocket ship is three times its rest energy, what is its speed?
a.
b.
c.
d.
e.
0.72c
0.87c
0.94c
0.97c
none of the above
10. When light of wavelength 350 nm falls on a potassium surface, electrons are emitted that have a
maximum kinetic energy of 1.31 eV. Find the work function of potassium.
a.
b.
c.
d.
e.
2.24 eV
4.42 eV
6.24 eV
8.84 eV
none of the above
11. A hydrogen atom is in the first excited state (n = 2). Using the Bohr theory of the atom, find the
kinetic energy of the electron.
a.
b.
c.
d.
e.
1.2 eV
3.4 eV
5.4 eV
6.8 eV
13.6 eV
BB
12. What is the energy of the photon that, when absorbed by a singly ionized 42 He atom, can cause a
transition from n = 1 to n = 4?
a.
b.
c.
d.
e.
4.6 eV
14.2 eV
51.0 eV
108 eV
none of the above
13. A long, straight wire carries a steady current I. A rectangular conducting loop lies in the same
plane as the wire, with two sides parallel to the wire and two sides perpendicular. Suppose the
loop is pushed toward the wire as shown. Given the direction of I, the induced current in the loop
is
a. clockwise.
b. counterclockwise.
c. need more information
14. A cylindrical piece of insulating material is placed in an external electric field, as shown. The net
electric flux passing through the surface of the cylinder is
a. negative
b. positive
c. zero
U nucleus. The volume of a sphere is 4r3/3. Assume
that the proton and the neutron have the same mass, m = 1.67 x 10-27 kg.
15. Find the mass density of nucleons in a
a.
b.
c.
d.
e.
238
92
2.3 x104 kg/m3
2.3 x109 kg/m3
2.3 x1012 kg/m3
2.3 x1015 kg/m3
2.3 x1017 kg/m3
16. A metal wire has a resistance of 10.00  at a temperature of 20C. If the same wire has a
resistance of 10.55  at 90C, what is the resistance when its temperature is 20C? Hint: first
find the temperature coefficient of resistivity.
a. 0.70 
b. 9.69 
c. 10.31 
d. 13.8 
17. A physics professor can teach as long as 60% of his brain cells are alive and functioning. The
stress of teaching causes brain cells to die with an average half-life of 30 years. Assume that brain
cells don’t reproduce or repair themselves and that there is no other source of brain-cell death.
How long can the professor go on teaching (approximately)?
a.
b.
c.
d.
e.
10 y
20 y
30 y
40 y
50 y
18. Determine X in the following reaction:
a.
b.
c.
d.
e.
A
Th 230
88 Ra  Z X (use the table below if necessary).
234
90
hydrogen
deuterium
tritium
helium
rustolium
19. A wire carries a steady current of 0.1 A over a period of 20 s. What total charge passes through the
wire in this time interval?
a. 200 C
b. 20 C
c. 2 C
d. 0.005 C
20. Determine the amount of energy released in the fusion reaction:
a.
b.
c.
d.
e.
2
1
H 13H 24He  10n
4.59 MeV
7.21 MeV
17.6 MeV
21.5 MeV
a lot
21. (bonus) A simple circuit consists of a resistor R, a capacitor C charged to a potential Vo, and a
switch that is initially open but then thrown closed. Immediately after the switch is thrown closed,
the current in the circuit is
a. Vo/R.
b. zero.
c. need more information
g = 9.8 m/s2
1 eV = 1.6 x 10-19 J
1 kWh = 3.60 x 106 J
c = 3.00 x 108 m/s
h = 6.63 x 10-34 J s
a0= 0.0529  9 m
1 u = 931.5 MeV
1 u = 1.66  27 kg
F=ma
KE 
1 2 p2
mv 
2
2m
q
E  ke
2
ke=8.99 x 109 Nm2/C2
 = 8.85 x 10-12 C2/Nm2
     Tm/A
me= 9.11 x 1031 kg
  1.05  10 34 J s
RH =1.097   m-1
r0 = 1.2  15 m
a


p  mv
v2
r
F  ke
KEf +PEf = KEi + PEi
V  ke
q
r
q1 q 2
r2
Q  CV
r
1
1
1



Ceq C1 C2
C eq  C1  C 2  
V  IR
1
1
1



Req R1 R2
F  qvB sin 
F  BI sin 
B
 0 NI

E  NAB sin t 
 
1
H
Mass (u)
1.007825
n
1.008665
H
2.014102
H
3.016049
He
4.002602
1
1
0
1
2
1
3
1
4
2
238
92

t
  2f
  B A  BA cos 
E  N
E max  NAB
U
238.050784




p1i  p2i  p1 f  p2 f
E
F
q0
C  0
A
d
Req  R1  R2  
B
0 I
2r
E  Bv
c  f
t  t P
L  LP 
p  mv
E  mc 2
h
p

ke2
E
2r
KE  mc 2  mc 2
E 2  p 2c2  m2c4
hc
E

En  nhf
2
mke2
Ei  E f  E  hf
1  v2 c2
a0 
2
me k e Z 2 e 4  1 
 2
2 2
n 
ln( 2) 0.693




KEmax  hf  
KE 
ke2
2r
En  
r  r0 A1 / 3
T1 / 2
E  mc 2
mvr  n
 1
1 
 RH  2  2 
n

ni 
 f
N
R
 N
t
1
E  KE  PE
r  n 2 a0 / Z
En  
Z2
(13.6 eV)
n2
N  N 0 e  t