klarin (sjk772) – oldhomework 10 – Turner – (56705)
1
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print-out
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have
12
questions.
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before answering.
001
(part 1 of 4) 10.0 points
An air-filled capacitor consists of two parallel
plates, each with an area of 4
.
3 cm
2
,
sepa-
rated by a distance 1
.
5 mm
.
A 15 V potential
difference is applied to these plates.
The permittivity of a vacuum is 8
.
85419
×
10
−
12
C
2
/
N
·
m
2
. 1 pF is equal to 10
−
12
F
.
The magnitude of the electric field between
the plates is
1.
E
=
V
d
.
correct
2.
E
=
V d .
3.
E
=
1
(
V d
)
2
.
4.
E
= (
V d
)
2
.
5.
E
=
parenleftbigg
d
V
parenrightbigg
2
.
6.
E
=
1
V d
.
7.
E
=
d
V
.
8.
E
=
parenleftbigg
V
d
parenrightbigg
2
.
9.
None of these
Explanation:
Since
E
is constant between the plates,
V
=
integraldisplay
vector
E
·
d
vector
l
=
E d
E
=
V
d
.
002
(part 2 of 4) 10.0 points
The magnitude of the surface charge density
on each plate is
1.
σ
=
ǫ
0
V d
2.
σ
=
ǫ
0
parenleftbigg
V
d
parenrightbigg
2
.
3.
σ
=
ǫ
0
V d
.
4.
σ
=
ǫ
0
(
V d
)
2
.
5.
σ
=
ǫ
0
(
V d
)
2
.
6.
σ
=
ǫ
0
parenleftbigg
d
V
parenrightbigg
2
.
7.
None of these
8.
σ
=
ǫ
0
V
d
.
correct
9.
σ
=
ǫ
0
d
V
.
Explanation:
Use Gauss’s Law. We find that a pillbox of
cross section
S
which sticks through the sur-
face on one of the plates encloses charge
σ S.
The flux through the pillbox is only through
the top, so the total flux is
E S.
Gauss’ Law
gives
σ
=
ǫ
0
E
=
ǫ
0
V
d
Alternatively, we could just recall this result
for an infinite conducting plate (meaning we
neglect edge effects) and apply it.
003
(part 3 of 4) 10.0 points
Calculate the capacitance.
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klarin (sjk772) – oldhomework 10 – Turner – (56705)
2
Correct answer: 2
.
5382 pF.
Explanation:
Let :
A
= 0
.
00043 m
2
,
d
= 0
.
0015 m
,
V
= 15 V
,
and
ǫ
0
= 8
.
85419
×
10
−
12
C
2
/
N
·
m
2
.
The capacitance is given by
C
=
ǫ
0
A
d
= 8
.
85419
×
10
−
12
C
2
/
N
·
m
2
×
0
.
00043 m
2
0
.
0015 m
= 2
.
5382
×
10
−
12
F
=
2
.
5382 pF
.
004
(part 4 of 4) 10.0 points
Calculate plate charge;
i.e.
, the magnitude of
the charge on each plate.
Correct answer: 38
.
073 pC.

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- Fall '10
- Turner
- Electrostatics, Work, Correct Answer, Electric charge
-
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