Physics 8.02
TEST 3 MASHUP
November 26, 2002
PLEASE DETACH THIS SHEET
AND USE AT YOUR CONVENIENCE
Some (possibly useful) Relations:
F
=
1
4
πε
o
q
1
q
2
r
2
E
=
q
4
πε
o
r
2
ˆ
r
observer
to
source
from
points
r
ˆ
∫
=
⋅
surface
closed
o
inside
Q
ε
dA
E
outside
to
inside
from
points
dA
∫
⋅
−
=
−
=
∆
b
a
a
b
b
to
a
from
moving
V
V
V
ds
E
j
i
q
q
U
i
j
j
i
o
j
i
≠
−
=
∑∑
,
4
2
1
r
r
πε
C
≡
Q
∆
V
U =
1
2
C
∆
V
2
=
Q
2
2C
d
A
o
plate
parallel
ε
κ
=
C
τ
=
RC
∆
V
=
i R
L
L
R
A
A
ρ
σ
=
=
P
joule
=
i
∆
V = i
2
R
=
∆
V /R
2
2
ˆ
4
o
q
r
µ
π
×
=
v
r
B
2
ˆ
4
o
I
r
µ
π
×
=
ds
r
dB
F
=
q
v
×
B
ext
ext
I
=
×
dF
ds
B
ττ
=
µµ ×
B
N I A
µ
=
through
o
I
µ
=
⋅
∫
ds
B
∫
∫
⋅
−
=
⋅
dA
B
ds
E
dt
d
ε
=
–
N
d
φ
B
dt
L
=
N
φ
B
i
ε
=
–
L
di
dt
∫
=
⋅
0
dA
B
τ
=
L
/
R
U
L
=
1
2
L i
2
u
B
=
|
B
|
2
2
µ
0
T
=
2
π
ω
=
1
f
if
ε
(t) =
ε
m
sin(
ω
t ), then
i (t) = i
m
sin(
ω
t
-
φ
),
where
i
m
=
ε
m
R
2
+
ω
L –
1
ω
C
2
1/2
and
tan
φ
=
ω
L –
1
ω
C
R
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