dzifanu (sd26397) – Hw 3 – opyrchal – (121102)
1
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printout
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have
14
questions.
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before answering.
001(part1of3)10.0points
An electric field of magnitude 2170 N
/
C is
applied along the
x
axis.
Calculate the electric flux through a rect
angular plane 0
.
451 m wide and 0
.
7 m long if
the plane is parallel to the
yz
plane.
Correct answer: 685
.
069 N
·
m
2
/
C.
Explanation:
Let :
E
= 2170 N
/
C
,
θ
= 0
◦
,
L
= 0
.
7 m
,
and
W
= 0
.
451 m
.
The area of the rectangle is
A
=
L W
= (0
.
7 m) (0
.
451 m)
= 0
.
3157 m
2
.
Since the field is uniform,the flux is
φ
=
E
·
A
=
E A
cos
θ
= (2170 N
/
C) (0
.
3157 m
2
) (cos 0
◦
)
=
685
.
069 N
·
m
2
/
C
.
002(part2of3)10.0points
Calculate the electric flux through the same
rectangle, if it is parallel to the
xy
plane.
Correct answer: 0 N
·
m
2
/
C.
Explanation:
The angle is
θ
= 90
◦
,cos
θ
= 0
,
and
φ
=
E
·
A
=
E A
cos
θ
= (2170 N
/
C) (0
.
3157 m
2
) (0)
=
0 N
·
m
2
/
C
.
003(part3of3)10.0points
Calculate the electric flux through the same
rectangle, but now the rectangle contains the
y
axis and its normal makes an angle of 43
◦
with the
x
axis.
Correct answer: 501
.
028 N
·
m
2
/
C.
Explanation:
Let
θ
= 43
◦
φ
=
E
·
A
=
E A
cos
θ
= (2170 N
/
C) (0
.
3157 m
2
) (cos 43
◦
)
=
501
.
028 N
·
m
2
/
C
.
004
10.0points
A closed surface with dimensions
a
=
b
=
0
.
522 m and
c
= 0
.
783 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
= 3 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
.
03541
×
10
−
11
C.
Explanation:
Let :
a
=
b
= 0
.
522 m
,
c
= 0
.
783 m
,
α
= 2 N
/
C
,
and
β
= 3 N
/
(C m
2
)
.
The electric field throughout the region is
directed along the
x
axis and the direction of
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dzifanu (sd26397) – Hw 3 – opyrchal – (121102)
2
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.
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 Spring '09
 PRODAN
 Physics, Cartesian Coordinate System, Correct Answer, Electric charge

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