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nguyen (jmn727) – homework 06 – Turner – (59070)
1
This printout should have 11 questions.
Multiplechoice questions may continue on
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beFore answering.
001
10.0 points
A 114 cm diameter loop is rotated in a uniForm
electric feld until the position oF maximum
electric ±ux is Found. The ±ux in this position
is measured to be 6
.
12
×
10
5
N
·
m
2
/
C.
What is the electric feld strength?
Correct answer: 5
.
99587
×
10
5
N
/
C.
Explanation:
Let :
r
= 57 cm = 0
.
57 m
and
Φ = 6
.
12
×
10
5
N
·
m
2
/
C
.
By Gauss’ law,
Φ =
c
v
E
·
d
v
A
The position oF maximum electric ±ux will be
that position in which the plane oF the loop is
perpendicular to the electric feld;
i.e.
, when
v
E
·
d
v
A
=
E dA
. Since the feld is constant,
Φ =
E A
=
Eπ r
2
E
=
Φ
π r
2
=
6
.
12
×
10
5
N
·
m
2
/
C
π
(0
.
57 m)
2
=
5
.
99587
×
10
5
N
/
C
.
002
10.0 points
A (7 m by 7 m) square base pyramid with
height oF 4
.
45 m is placed in a vertical electric
feld oF 55
.
1 N
/
C.
b
7 m
4
.
45 m
55
.
1 N
/
C
Calculate the total electric ±ux which goes
out through the pyramid’s Four slanted sur
Faces.
Correct answer: 2699
.
9 N m
2
/
C.
Explanation:
Let :
s
= 7 m
,
h
= 4
.
45 m
,
and
E
= 55
.
1 N
/
C
.
By Gauss’ law,
Φ =
v
E
·
v
A
Since there is no charge contained in the pyra
mid, the net ±ux through the pyramid must
be 0 N/C. Since the feld is vertical, the ±ux
through the base oF the pyramid is equal and
opposite to the ±ux through the Four sides.
Thus we calculate the ±ux through the base
oF the pyramid, which is
Φ =
E A
=
E s
2
= (55
.
1 N
/
C) (7 m)
2
=
2699
.
9 N m
2
/
C
.
003
10.0 points
A spherical shell oF radius 4
.
3 m is placed
in a uniForm electric feld with magnitude
3570 N
/
C.
Determine the total electric ±ux through
the shell.
Correct answer: 0 N
·
m
2
/
C.
Explanation:
Let :
r
= 4
.
3 m
and
E
= 3570 N
/
C
.
The uniForm feld enters the shell on one side
and exits on the other, so the total ±ux is zero:
Φ =
c
v
E
·
d
v
A
=
0
.
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This note was uploaded on 01/21/2010 for the course PHY 303L taught by Professor Turner during the Spring '08 term at University of Texas at Austin.
 Spring '08
 Turner
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