Nguyen, Thanh – Homework 7 – Due: Feb 15 2008, 7:00 pm – Inst: Weathers
1
This
printout
should
have
16
questions.
Multiplechoice questions may continue on
the next column or page – find all choices
before answering.
The due time is Central
time.
001
(part 1 of 1) 10 points
Two conductors insulated from each other are
charged by transferring electrons from one
conductor to the other.
After 1
.
401
×
10
13
have been transferred, the potential difference
between the conductors is 16
.
3 V.
The
charge
on
an
electron
is

1
.
60218
×
10

19
C
.
What is the capacitance of the system?
Correct answer: 1
.
37709
×
10

7
F.
Explanation:
Let :
e
=

1
.
60218
×
10

19
C
,
N
= 1
.
401
×
10
13
electrons
,
and
V
= 16
.
3 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
=

(1
.
401
×
10
13
) (

1
.
60218
×
10

19
C)
16
.
3 V
=
1
.
37709
×
10

7
F
.
keywords:
002
(part 1 of 1) 10 points
A spherical capacitor consists of a conducting
ball of radius 4 cm that is centered inside a
grounded conducting spherical shell of inner
radius 8 cm.
The
Coulomb
constant
is
8
.
98755
×
10
9
N m
2
/
C
2
.
What charge is required to achieve a poten
tial of 876 V on the ball of radius 4 cm?
Correct answer: 7
.
79745
×
10

9
C.
Explanation:
Let :
k
e
= 8
.
98755
×
10
9
N m
2
/
C
2
,
a
= 4 cm = 0
.
04 m
,
b
= 8 cm = 0
.
08 m
and
V
= 876 V
.
The capacitance of a spherical capacitor is
given by
C
=
a b
k
e
(
b

a
)
. The charge required
to achieve a potential difference
V
between
the shell and the ball is given by
Q
=
C V
=
1
k
e
a b V
(
b

a
)
=
1
(8
.
98755
×
10
9
N m
2
/
C
2
)
×
(0
.
04 m) (0
.
08 m) (876 V)
(0
.
08 m)

(0
.
04 m)
=
7
.
79745
×
10

9
C
.
keywords:
003
(part 1 of 2) 10 points
A 20 m length of coaxial cable has a solid
cylindrical wire inner conductor with a di
ameter of 1
.
192 mm and carries a charge of
7
.
31
μ
C.
The surrounding conductor is a
cylindrical shell and has an inner diameter of
10
.
515 mm and a charge of

7
.
31
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: 0
.
511053 nF.
Explanation:
Let :
k
e
= 8
.
98755
×
10
9
N
·
m
2
/
C
2
,
Q
= 7
.
31
μ
C
,
‘
= 20 m
,
a
= 1
.
192 mm
,
and
b
= 10
.
515 mm
.
The charge per unit length is
λ
≡
Q
‘
.
V
=

Z
b
a
~
E
·
d~s
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Nguyen, Thanh – Homework 7 – Due: Feb 15 2008, 7:00 pm – Inst: Weathers
2
=

2
k
e
λ
Z
b
a
dr
r
=

2
k
e
Q
‘
ln
b
a
¶
.
The capacitance of a cylindrical capacitor
is given by
C
≡
Q
V
=
‘
2
k
e
1
ln
b
a
¶
=
20 m
2 (8
.
98755
×
10
9
N
·
m
2
/
C
2
)
×
1
ln
10
.
515 mm
1
.
192 mm
¶
·
1
×
10
9
nF
1 F
¶
=
0
.
511053 nF
004
(part 2 of 2) 10 points
What is the potential difference between the
two conductors?
Correct answer: 14
.
3038 kV.
Explanation:
Therefore
V
=
Q
C
=
7
.
31
μ
C
0
.
511053 nF
1
×
10
9
nF
1 F
¶
×
1 C
1
×
10
6
μ
C
¶
1 kV
1000 V
¶
=
14
.
3038 kV
keywords:
005
(part 1 of 1) 10 points
The plates of a parallelplate capacitor are
separated by 0
.
111 mm.
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 Spring '00
 Littler
 Work, Correct Answer, μF, Thanh

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