nguyen (jmn727) – oldhomework 33 – Turner – (59070)
1
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printout
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have
12
questions.
Multiplechoice questions may continue on
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before answering.
001
(part 1 of 2) 10.0 points
A 0
.
3071 A current is charging a capacitor
that has circular plates, 11
.
14 cm in radius.
The plate separation is 3
.
49 mm.
The permitivity or free space is 8
.
85
×
10

12
and the permeability of free space is 1
.
25664
×
10

6
T
·
m
/
A.
What is the time rate of increase of electric
field between the plates?
Correct answer: 8
.
90054
×
10
11
V
/
m s.
Explanation:
Let :
I
= 0
.
3071 A
,
r
= 11
.
14 cm = 0
.
1114 m
,
A
=
π r
2
= 0
.
038987 m
2
,
and
ǫ
0
= 8
.
85
×
10

12
.
Let Φ
E
be the flux of the electric field, defined
as Φ
E
=
integraldisplay
vector
E
·
d
vector
A
. Thus
d
Φ
E
dt
=
d
dt
(
E A
) =
I
ǫ
0
Time rate of increase of electric field between
the plates is
P
=
d E
dt
=
I
ǫ
0
A
=
0
.
3071 A
(8
.
85
×
10

12
)(0
.
038987 m
2
)
=
8
.
90054
×
10
11
V
/
m s
.
002
(part 2 of 2) 10.0 points
What is the magnetic field between the plates
0
.
0595 m from the center?
Correct answer: 2
.
9448
×
10

7
T.
Explanation:
Let :
r
= 0
.
0595 m
and
μ
0
= 1
.
25664
×
10

6
T
·
m
/
A
.
Since
contintegraldisplay
vector
B
·
dvectors
=
ǫ
0
μ
0
d
dt
Φ
E
Then magnetic field,
B
,at the distance
r
from
the center between the plates satisfies
2
π r B
=
ǫ
0
μ
0
d
dt
parenleftbigg
Q
ǫ
0
A
π r
2
parenrightbigg
Hence
B
=
μ
0
I r
2
A
=
(0
.
3071 A)(0
.
0595 m)
2(0
.
038987 m
2
)
×
(1
.
25664
×
10

6
T
·
m
/
A)
=
2
.
9448
×
10

7
T
.
003
10.0 points
A sinusoidal voltage is applied directly across
a 19
.
23
μ
F capacitor.
The frequency of the
source is 5
.
2 kHz, and the voltage amplitude
is 41
.
4 V.
Find the maximum value of the displace
ment current in the capacitor.
Correct answer: 26
.
0113 A.
Explanation:
Let :
C
= 19
.
23
μ
F = 1
.
923
×
10

5
F
,
f
= 5
.
2 kHz = 5200 Hz
,
and
V
max
= 41
.
4 V
.
The angular frequency of the source is
ω
= 2
π f
= 2
π
(5200 Hz)
= 32672
.
6 s

1
.
The voltage across the capacitor as a function
of
t
is
V
=
V
max
sin(
ω t
)
= (41
.
4 V) sin
bracketleftbig
(32672
.
6 s

1
)
t
bracketrightbig
.
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nguyen (jmn727) – oldhomework 33 – Turner – (59070)
2
Now we can find the charge on the capacitor,
Q
=
CV
, and to calculate the displacement
current
I
d
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 Spring '08
 Turner
 Current, Work, Light, Speed of light, Correct Answer

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