Exam3_2002Fall - Physics 8.02 TEST 3 MASHUP PLEASE DETACH...

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