1
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Physics
8.02
Spring 2008
Exam Two Equation Sheet
Force Laws:
(
)
ext
ext
q
=
+
×
F
E
v
B
G
G
G
G
Source Equations:
2
1
ˆ
4
o
dq
d
r
πε
=
E
r
G
2
ˆ
4
o
I d
d
r
µ
π
×
=
s
r
B
G
G
ˆ
r
r
r =
G
points from source to field point
Current Density and Current:
open surface
I
d
=
⋅
∫∫
J
a
G
G
Gauss’s Law:
inside
closedsurface
/
o
d
Q
ε
⋅
=
∫∫
E
A
G
G
w
Ampere’s Law:
closed path
open surface
o
d
d
µ
⋅
=
⋅
∫
∫∫
B
s
J
a
G
G
G
G
v
Gauss’s Law for Magnetism:
0
closed
surface
d
⋅
=
∫∫
B
A
G
G
w
Electric Potential Difference:
b
b
a
a
V
V
V
d
∆
=
−
≡ −
⋅
∫
E
s
G
G
Capacitance:
V
Q
C
∆
=
2
2
1
1
2
2
Q
U
C
V
C
=
=
∆
Capacitors in Parallel:
1
2
eq
C
C
C
=
+
+⋅⋅⋅
Capacitors in Series:
1
2
1
1
1
eq
C
C
C
=
+
+⋅⋅⋅
Ohm’s Law:
V
I R
∆
=
where
is the conductivity
c
c
σ
σ
=
J
E
G
G
where
is the resistivity
r
r
ρ
ρ
=
E
J
G
G
Resistors in Parallel:
1
2
1
1
1
eq
R
R
R
=
+
+⋅⋅⋅
Resistors in Series:
1
2
eq
R
R
R
=
+
+⋅⋅⋅
Joule Heating:
2
2
Joule
/
P
I
V
I R
V
R
=
∆
=
= ∆
Magnetic Dipoles
:
=
I A
μ
n
G
±
Torque:
=
×
τ
μ
B
G
G
G
Force:
(
/
)
z
z
z
F
dB
dz
µ
=
Cross-products of unit vectors
:
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
0
×
=
×
=
×
=
i
i
j
j
k
k
ˆ
ˆ
ˆ
×
=
i
j
k
ˆ
ˆ
ˆ
×
=
j
k
i
ˆ
ˆ
ˆ
×
=
k
i
j
Kinematics:
2
/
cent
v
r
=
a
G
;
2
2
/
f
T
ω
π
π
=
=
Circumferences, Areas,
Volumes:
1)
Circle radius
r
: Area
π
r
2
;
Circumference
2
π
r
2)
Sphere of radius
r
: Surface Area
4
π
r
2
; Volume
(4 / 3)
π
r
3
Cylinder of radius
r
and length
l
:
Area
2
rl
π
; Volume
2
r l
π
Integrals :
dr
a
b
∫
=
b
−
a
;
1
ln( /
)
b
a
r
dr
b a
−
=
∫
2
(1/
1/
)
b
a
r
dr
a
b
−
=
−
∫
Constants:
9
2
-2
0
1/ 4
9
10 N m
C
e
k
πε
=
=
×
⋅
⋅
7
-1
0
/ 4
10
T m A
µ
π
−
=
⋅
⋅

This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*
2

3
8.02 Exam Two Spring 2008 Solutions
FAMILY (last)
NAME
GIVEN (first) NAME
Student ID Number
Your Section:
____L01 MW 9 am
____L02 MW 11 am
____L03 MW 1 pm
____L04 MW 3 pm
____L05 TTh 9 am
____L06 TTh 11 am
____L07 TTh 1 pm
____L08 TTh 3 pm
Your Group (e.g. 10A):
______________
Score
Grader
Section 1
(25 points)
Problem 1 (25 points)
Problem 2 (25 points)
Problem 3 (25 points)
TOTAL

This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*