fierro (jmf2547) – HW 06 – berk – (60290)
1
This
printout
should
have
11
questions.
Multiplechoice questions may continue on
the next column or page – find all choices
before answering.
001
10.0 points
A closed surface with dimensions
a
=
b
=
0
.
554 m and
c
= 0
.
6648 m is located as in
the figure.
The electric field throughout the
region is nonuniform and given by
vector
E
= (
α
+
β x
2
)ˆ
ı
where
x
is in meters,
α
= 2 N
/
C, and
β
= 4 N
/
(C m
2
).
E
y
x
z
a
c
b
a
What is the magnitude of the net charge
enclosed by the surface?
Correct answer: 1
.
28109
×
10
−
11
C.
Explanation:
Let :
a
=
b
= 0
.
554 m
,
c
= 0
.
6648 m
,
α
= 2 N
/
C
,
and
β
= 4 N
/
(C m
2
)
.
The electric field throughout the region is
directed along the
x
axis and the direction of
d
vector
A
is perpendicular to its surface. Therefore,
vector
E
is parallel to
d
vector
A
over the four faces of
the surface which are perpendicular to the
yz
plane, and
vector
E
is perpendicular to
d
vector
A
over
the two faces which are parallel to the
yz
plane.
That is, only the left and right sides
of the right rectangular parallel piped which
encloses the charge will contribute to the flux.
The net electric flux through the cube is
ΔΦ =
integraldisplay
right side
E
x
d A
⊥

integraldisplay
left side
E
x
d A
⊥
=
a b
bracketleftbig
α
+
β
(
a
+
c
)
2

α

β a
2
bracketrightbig
=
a b β
(2
a c
+
c
2
)
=
a b c β
(2
a
+
c
)
= (0
.
554 m) (0
.
554 m) (0
.
6648 m)
×
[4 N
/
(C m
2
)] [2 (0
.
554 m) + 0
.
6648 m]
= 1
.
44687 N m
2
/
C
,
so the enclosed charge is
q
=
ǫ
0
ΔΦ
= [8
.
85419
×
10
−
12
C
2
/
(N m
2
)]
×
(1
.
44687 N m
2
/
C)
=
1
.
28109
×
10
−
11
C
.
002
10.0 points
Which of the following is true about the net
force on an uncharged conducting sphere in a
uniform electric field?
1.
It produces a torque on the sphere about
the direction of the field.
2.
It is zero.
correct
3.
It is in the direction opposite to the field.
4.
It causes the sphere to oscillate about an
equilibrium position.
5.
It is in the direction of the field.
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 Spring '08
 Turner
 Charge, Electrostatics, Magnetic Field, Electric charge

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