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Physics 8.02
Final Exam
Spring 2004
Some (possibly useful) Relations:
enclosed
o
closed
surface
Q
d
ε
⋅=
∫∫
EA
G
G
w
total
closed
open
path
surface
external
self
open
surface
d
dd
dt
d
d
dt
−
⋅
⎡⎤
=−
+
⋅
⎣⎦
∫
Es
B
A
BB
G
GG
G
G
v
A
0
closed
surface
d
BA
G
G
w
closed
path
thru
o
E
E
open
surface
d
d
I
dt
where
d
µµε
+Φ
Φ=
⋅
∫
oo
Bs
G
G
G
G
v
2
0
1
2
elec
uE
=ε
2
0
1
2
mag
uB
=
µ
0
2
ˆ
4
µ
π
×
==
sr
source
source
Id
d
r
G
q
qq
=+×
FEv
G
B
G
B
dI
d
=×
Fs
G
0
1
ˆ
4
2
dq
r
πε
=
dE
r
G
2
0
1
ˆ
4
V
dq
r
=
∫
Er
G
2
1
2
1
P
21
P
The electric potential at point P
minus that at point P is given by
V(P )
d
−=
−
⋅
∫
G
G
iN
i
i1
0i
,
q
1
V
4r
=
=
∆=
P
∑
VI
R
22
Joule Heating
PI
R
V
∆
/
R
QCV
=
∆
2
2
capacitor
1
Q
UC
V
C
=∆=
self field
self
one turn
Nd
L
I
G
G
2
inductor
1
2
UL
=
I
0
1
LC
=
ω
00
1
c
=
µ ε
1
f
T
=
f
T
ω= π = π
2
k
= πλ
cTf k
=
λ=
ω
0
1
=
×
µ
SE
G
B
G
G
DOUBLE SLIT:
constructive:
sin
,
0,
1,
2,
3, .
..
dm
m
θ=
λ
=
±
±
±
destructive:
1
sin
,
0,
2,
3, .
.
2
dm m
⎛⎞
+
λ
=
±
±
±
⎜⎟
⎝⎠
SINGLE SLIT:
destructive:
sin
,
2,
3, .
..
an
n
θ= λ
=±
±
±
Areas, Volumes, etc.:
1) The area of a circle
of radius
r
is
π
r
2
Its
circumference is
2
r
2)
The surface area of a
sphere of radius
r
is
4
r
2
.
Its volume is
3
3
r
4
3) The area of the sides
of a cylinder of
radius
r
and height
h
is
2
r h.
Its volume
is
r
2
h
USEFUL INTEGRALS:
d
c
dx
d
c
∫
()
1
2
d
c
rdr
d
c
∫
1
ln
d
c
d
dr
rc
=
⎢⎥
∫
2
11
d
c
dr
1
d
⎡
⎤⎛
⎞
⎣
⎦⎝
∫
⎠
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2
8.02 Final Exam Spring 2004
FAMILY (last)
NAME
GIVEN (first) NAME
Student ID Number
Your Section (check one):
___MW 10 am
____MW 12 noon
____MW 2 pm
___TTh 10 am
____TTh 12 noon
____TTh 2 pm
Your Group (e.g. 10A):
_________
Problem
Score
Grader
1 (30 points)
2 (30 points)
3 (30 points)
4 (25 points)
5 (35 points)
6 (30 points)
TOTAL
2
MIT PHYSICS DEPARTMENT
`
page
3
Problem 1:
Ten Conceptual Questions.
Circle your choice for the correct answer to
the ten questions.
Question A (3 points):
The figure below shows an “iron filings” representation of the
field of a magnetic dipole plus a constant field.
The constant field points to the upper
right corner of the image.
If the magnetic dipole is free to rotate, then the dipole will
a) Not rotate since the torque on the dipole is zero in a uniform field
b) Rotate clockwise
c) Rotate counterclockwise
d)
Impossible to tell without more information
Question B (3 points):
In the circuits below, all of the batteries and light bulbs are identical.
A
B
C
Let the light put out by the
top
bulb in each of the above circuits be
A
P
,
, and
,
respectively.
Then
B
P
C
P
a)
A
BC
PPP
==
b)
A
>=
c)
A
<=
d)
BA
C
C
B
e)
f)
CA
<
=
g)
B
h)
A
<
<
3
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Question C (3 points):
Five loops are formed of lengths of identical cooper wire.
Loops 1, 2, 3 and 4 have
exactly the same dimensions; loop 5 has the same height as the others but is longer. At
the instant shown in the figure, all the loops are moving at the same speed in the
directions indicated.
There is a uniform magnetic field pointing out of the page in region
I; in region II there is no magnetic field. Ignore any interactions between the loops.
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This note was uploaded on 04/07/2008 for the course 8 8.02 taught by Professor Hudson during the Spring '07 term at MIT.
 Spring '07
 Hudson

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