tovar (jdt436) – homework 12 – Turner – (59070)
1
This printout should have 12 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 parallelplate capacitor oF dimensions
1
.
92 cm
×
3
.
36 cm is separated by a 0
.
8 mm
thickness oF paper.
±ind the capacitance oF this device. The
dielectric constant
κ
For paper is 3.7.
Correct answer: 26
.
4181 p±.
Explanation:
Let :
κ
= 3
.
7
,
d
= 0
.
8 mm = 0
.
0008 m
,
and
A
= 1
.
92 cm
×
3
.
36 cm = 0
.
00064512 m
2
.
We apply the equation For the capacitance oF
a parallelplate capacitor and fnd
C
=
κǫ
0
A
d
= (3
.
7) (8
.
85419
×
10
−
12
C
2
/
N
·
m
2
)
×
p
0
.
00064512 m
2
0
.
0008 m
P
1
×
10
12
p±
1 ±
=
26
.
4181 p±
.
002
(part 2 oF 2) 10.0 points
What is the maximum charge that can be
placed on the capacitor? The electric strength
oF paper is 1
.
6
×
10
7
V
/
m.
Correct answer: 0
.
338151
μ
c.
Explanation:
Let :
E
max
= 1
.
6
×
10
7
V
/
m
.
Since the thickness oF the paper is 0
.
0008 m,
the maximum voltage that can be applied
beFore breakdown is
V
max
=
E
max
d.
Hence, the maximum charge is
Q
max
=
C V
max
=
C E
max
d
= (26
.
4181 p±)(12800 V)
·
1
×
10
−
12
±
1 p±
·
1
×
10
6
μ
C
1 C
=
0
.
338151
μ
c
.
003
(part 1 oF 4) 10.0 points
Determine the total energy stored in a con
ducting sphere with charge
Q
.
Hint:
Use the capacitance Formula For
a spherical capacitor which consists oF two
spherical shells.
Take the inner sphere to
have a radius
a
and the outer shell to have an
infnite radius.
1.
U
=
Q
2
8
π ǫ
0
a
2
2.
U
=
Q
2
π
8
ǫ
0
a
3.
U
=
Q
2
4
π ǫ
0
a
4.
U
=
Q
8
π ǫ
0
a
5.
U
=
Q
2
a
4
π ǫ
0
6.
U
=
Q
2
8
π ǫ
0
a
correct
7.
U
=
Q
2
16
π ǫ
0
a
8.
U
=
Q
2
a
Explanation:
The capacitance Formula For a spherical ca
pacitor oF inner radius
a
and outer radius
b
is
C
=
a b
k
e
(
b

a
)
.
IF we let
b
→ ∞
, we fnd we can neglect
a
in
the denominator compared to
b
, so
C
→
a
k
e
= 4
π ǫ
0
a .
The total energy stored is
U
=
Q
2
2
C
=
Q
2
8
π ǫ
0
a
.
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2
004
(part 2 of 4) 10.0 points
Find the energy stored in a capacitor of charge
Q
±lled with dielectric, use
C
κ
=
κC
.
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 Spring '08
 Turner
 Capacitance, Energy, Work, Electric charge, Tovar

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