benavides (jjb2356) – homework 04 – Turner – (59130)
1
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printout
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11
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001
(part 1 of 2) 10.0 points
A charge
Q
is distributed uniformly along the
x
axis from
x
1
to
x
2
.
The
Coulomb
constant
is
8
.
98755
×
10
9
N
·
m
2
/
C
2
Which of the following integrals is correct
for the magnitude of the electric field at
x
0
on
the
x
axis? Assume that
x
0
> x
2
> x
1
and
k
e
=
1
4
πǫ
0
.
1.
None of these
2.
integraldisplay
x
2
x
1
k
e
Q
(
x
2
−
x
1
)
x
2
dx
3.
integraldisplay
x
2
x
1
k
e
Q
(
x
2
−
x
1
)(
x
0
−
x
)
2
dx
correct
4.
integraldisplay
x
2
x
1
k
e
Q
(
x
2
−
x
0
)(
x
0
−
x
)
2
dx
5.
integraldisplay
x
2
x
1
k
e
Q
(
x
2
−
x
0
)
x
2
dx
Explanation:
For a continuous charge distribution,
dE
=
k
e
dq
r
2
.
Recall that for a uniform linear charge dis
tribution,
dq
=
λ dx
=
Q
L
dx
=
Q
x
2
−
x
1
dx .
Furthermore, the point
x
0
is a distance
(
x
0
−
x
) from a charge element
dq
.
Hence
integrating from
x
=
x
1
to
x
=
x
2
yields
E
=
integraldisplay
x
2
x
1
k
e
Q
(
x
2
−
x
1
)(
x
0
−
x
)
2
dx .
002
(part 2 of 2) 10.0 points
If
x
1
= 0 m,
x
2
= 3
.
36 m and the charge
Q
= 2
.
44
μ
C, what is the magnitude
E
of the
electric field at
x
0
= 10
.
7 m?
Correct answer: 279
.
223 N
/
C.
Explanation:
Let :
k
e
= 8
.
98755
×
10
9
N
·
m
2
/
C
2
,
x
1
= 0 m
,
x
2
= 3
.
36 m
,
x
0
= 10
.
7 m
,
and
Q
= 2
.
44
μ
C
.
E
=
integraldisplay
x
2
x
1
k
e
Q
(
x
2
−
x
1
)(
x
0
−
x
)
2
dx
=
k
e
Q
(
x
2
−
x
1
)(
x
0
−
x
)
vextendsingle
vextendsingle
vextendsingle
vextendsingle
x
2
x
1
=
(
8
.
98755
×
10
9
N
·
m
2
/
C
2
)
(3
.
36 m
−
0 m)
×
(2
.
44
×
10
−
6
C)
×
bracketleftbigg
1
10
.
7 m
−
3
.
36 m
−
1
10
.
7 m
−
0 m
bracketrightbigg
=
279
.
223 N
/
C
.
003
(part 1 of 4) 10.0 points
Consider a disk of radius 4
.
2 cm with a uni
formly distributed charge of +4
μ
C.
Compute the magnitude of the electric field
at a point on the axis and 2
.
3 mm from the
center. The value of the Coulomb constant is
8
.
98755
×
10
9
N
·
m
2
/
C
2
.
Correct answer: 3
.
85311
×
10
7
N
/
C.
Explanation:
Let :
R
= 4
.
2 cm = 0
.
042 m
,
k
e
= 8
.
98755
×
10
9
N
·
m
2
/
C
2
,
Q
= 4
μ
C = 4
×
10
−
6
C
,
and
x
= 2
.
3 mm = 0
.
0023 m
.
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 Spring '08
 Turner
 Charge, Electrostatics, Work, Electric charge, Fundamental physics concepts, KE, Etot

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