johnson (rj6247) – hw 5 – Opyrchal – (121014)
1
This printout should have 17 questions.
Multiplechoice questions may continue on
the next column or page – fnd all choices
beFore answering.
001
(part 1 oF 2) 10.0 points
A 75 m length oF coaxial cable has a solid
cylindrical wire inner conductor with a di
ameter oF 3
.
142 mm and carries a charge oF
7
.
08
μ
C.
The surrounding conductor is a
cylindrical shell and has an inner diameter oF
7
.
928 mm and a charge oF

7
.
08
μ
C.
Assume the region between the conductors
is air. The Coulomb constant is 8
.
98755
×
10
9
N
·
m
2
/
C
2
.
What is the capacitance oF this cable?
Correct answer: 4
.
50811 n±.
Explanation:
Let :
k
e
= 8
.
98755
×
10
9
N
·
m
2
/
C
2
,
Q
= 7
.
08
μ
C
,
ℓ
= 75 m
,
a
= 3
.
142 mm
,
and
b
= 7
.
928 mm
.
The charge per unit length is
λ
≡
Q
ℓ
.
V
=

i
b
a
v
E
·
dvs
=

2
k
e
λ
i
b
a
dr
r
=

2
k
e
Q
ℓ
ln
p
b
a
P
.
The capacitance oF a cylindrical capacitor
is given by
C
≡
Q
V
=
ℓ
2
k
e
1
ln
p
b
a
P
=
75 m
2 (8
.
98755
×
10
9
N
·
m
2
/
C
2
)
×
1
ln
p
7
.
928 mm
3
.
142 mm
P
·
p
1
×
10
9
n±
1 ±
P
=
4
.
50811 n±
002
(part 2 oF 2) 10.0 points
What is the potential di²erence between the
two conductors?
Correct answer: 1
.
5705 kV.
Explanation:
ThereFore
V
=
Q
C
=
7
.
08
μ
C
4
.
50811 n±
p
1
×
10
9
n±
1 ±
P
×
p
1 C
1
×
10
6
μ
C
Pp
1 kV
1000 V
P
=
1
.
5705 kV
003
10.0 points
Two conductors insulated From each other are
charged by transFerring electrons From one
conductor to the other. AFter 2
.
621
×
10
13
have been transFerred, the potential di²erence
between the conductors is 14
.
6 V.
The
charge
on
an
electron
is

1
.
60218
×
10
−
19
C
.
What is the capacitance oF the system?
Correct answer: 2
.
87624
×
10
−
7
±.
Explanation:
Let :
e
=

1
.
60218
×
10
−
19
C
,
N
= 2
.
621
×
10
13
electrons
,
and
V
= 14
.
6 V
.
One conductor gains a charge oF
Q
=

N e
while the other gains a charge oF

Q.
The capacitance oF the system is
C
=
q
V
=

N e
V
=

(2
.
621
×
10
13
) (

1
.
60218
×
10
−
19
C)
14
.
6 V
=
2
.
87624
×
10
−
7
±
.
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View Full Documentjohnson (rj6247) – hw 5 – Opyrchal – (121014)
2
004
(part 1 of 2) 10.0 points
The potential diFerence between a pair of
oppositely charged parallel plates is 386 V.
a) If the spacing between the plates is dou
bled without altering the charge on the plates,
what is the new potential diFerence between
the plates?
Correct answer: 772 V.
Explanation:
Let :
d
2
= 2
d
1
and
Δ
V
1
= 386 V
.
The charge remains the same, so
Q
=
C
1
Δ
V
1
=
C
2
Δ
V
2
ε
0
A
d
1
Δ
V
1
=
ε
0
A
d
2
Δ
V
2
Δ
V
1
d
1
=
Δ
V
2
d
2
Δ
V
1
d
1
=
Δ
V
2
2
d
1
Δ
V
2
= 2Δ
V
1
= 2(386 V) =
772 V
.
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 Spring '08
 Opyrchal
 Work, Correct Answer

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