johnson (rj6247) – hw 3 – Opyrchal – (121014)
1
This printout should have 11 questions.
Multiplechoice questions may continue on
the next column or page – fnd all choices
beFore answering.
001
10.0 points
An electric feld oF magnitude 8000 N
/
C and
directed upward perpendicular to the Earth’s
surFace exists on a day when a thunderstorm
is brewing. A truck that can be approximated
as a rectangle 4
.
9 m by 4
.
6 m is traveling
along a road that is inclined 11
◦
relative to
the ground.
Determine the electric ±ux through the bot
tom oF the truck.
Correct answer: 1
.
77007
×
10
5
N
·
m
2
/
C.
Explanation:
Let :
E
= 8000 N
/
C
,
ℓ
= 4
.
9 m
,
w
= 4
.
6 m
,
and
θ
= 11
◦
.
By Gauss’ law,
Φ =
v
E
·
v
A
The ±ux through the bottom oF the car is
Φ =
E A
cos
θ
=
E ℓ w
cos
θ
= (8000 N
/
C) (4
.
9 m)
×
(4
.
6 m) cos(11
◦
)
=
1
.
77007
×
10
5
N
·
m
2
/
C
.
002
10.0 points
A nonconducting wall carries a uniForm
charge density oF 13
.
14
μ
C
/
cm
2
.
What is the electric feld 4
.
3 cm in Front oF
the wall?
Correct answer: 7
.
42022
×
10
9
N
/
C.
Explanation:
Let :
σ
= 13
.
14
μ
C
/
cm
2
and
r
= 4
.
3 cm
.
The electric feld oF an infnite plane oF surFace
charge density
σ
is
E
=
σ
2
ǫ
0
=
13
.
14
μ
C
/
cm
2
2 (8
.
85419
×
10
−
12
C
2
/
N
·
m
2
)
×
p
1 C
10
6
μ
C
P
·
p
100 cm
1 m
P
2
=
7
.
42022
×
10
9
N
/
C
.
003
(part 1 oF 2) 10.0 points
A thin spherical shell oF radius 4
.
93 m has a
total charge oF 8
.
11 C distributed uniFormly
over its surFace.
Let :
k
e
= 8
.
988
×
10
9
N
·
m
2
/
C
2
.
4
.
93 m
v
E
+
+
²ind the electric feld
v
E
11
.
7 m From the
center oF the shell (outside the shell).
Correct answer: 5
.
32491
×
10
8
N
/
C.
Explanation:
Let :
a
= 4
.
93 m
,
Q
= 8
.
11 C
,
and
r
= 11
.
7 m
.
IF we construct a spherical Gaussian surFace
oF radius
r > a
, concentric with the shell, then
the charge inside this surFace is
Q
. ThereFore
the feld at a point outside the shell is equiva
lent to that oF a point charge
Q
at the center.
²or
r > a
,
E
1
=
k Q
r
2
=
(8
.
988
×
10
9
N
·
m
2
/
C
2
)(8
.
11 C)
(11
.
7 m)
2
=
5
.
32491
×
10
8
N
/
C
.
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View Full Documentjohnson (rj6247) – hw 3 – Opyrchal – (121014)
2
004
(part 2 of 2) 10.0 points
Find the electric ±eld
E
2
3
.
13 m from the
center of the shell (inside the shell).
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 Spring '08
 Opyrchal
 Charge, Electrostatics, Work, Correct Answer, Electric charge, charge density

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