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howard (cah3459) – homework 06 – Turner – (56705)
1
This printout should have 9 questions.
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beFore answering.
001
10.0 points
A cubic box oF side
a
, oriented as shown, con
tains an unknown charge. The vertically di
rected electric feld has a uniForm magnitude
E
at the top surFace and 2
E
at the bottom
surFace.
a
E
2
E
How much charge
Q
is inside the box?
1.
Q
encl
=
1
2
&
0
Ea
2
2.
Q
encl
=2
&
0
2
3.
Q
encl
=3
&
0
2
4.
Q
encl
=0
5.
insu±cient inFormation
6.
Q
encl
=
&
0
2
correct
Explanation:
Electric ²ux through a surFace
S
is, by con
vention, positive For electric feld lines going
out of
the surFace
S
and negative For lines
going in.
Here the surFace is a cube and no ²ux goes
through the vertical sides.
The top receives
Φ
top
=

2
(inward is negative) and the bottom
Φ
bottom
2
.
The total electric ²ux is
Φ
E
=

2
+2
2
=
2
.
Using Gauss’s Law, the charge inside the
box is
Q
encl
=
&
0
Φ
E
=
&
0
2
.
002
10.0 points
A closed surFace with dimensions
a
=
b
=
0
.
435 m and
c
.
5655 m is located as in
the fgure. The electric feld throughout the
region is nonuniForm and given by
'
E
=(
α
+
β x
2
)ˆ
ı
where
x
is in meters,
α
= 5 N
/
C, and
β
= 2 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: 2
.
72015
×
10

12
C.
Explanation:
Let :
a
=
b
.
435 m
,
c
.
5655 m
,
α
= 5 N
/
C
,
and
β
= 2 N
/
(C m
2
)
.
The electric feld throughout the region is
directed along the
x
axis and the direction oF
d
'
A
is perpendicular to its surFace. ThereFore,
'
E
is parallel to
d
'
A
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 Fall '08
 Turner

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