song (shs546) – Homework 4 – weathers – (22202)
1
This printout should have 9 questions.
Multiplechoice questions may continue on
the next column or page – fnd all choices
beFore answering.
001 (part 1 of 2) 10.0 points
A uniFormly charged conducting plate with
area
A
has a total charge
Q
which is positive.
The fgure below shows a crosssectional view
oF the plane and the electric feld lines due to
the charge on the plane. The fgure is not
drawn to scale.
E
E
+
Q
P
±ind the magnitude oF the feld at point P,
which is a distance
a
From the plate. Assume
that
a
is very small when compared to the
dimensions oF the plate, such that edge e²ects
can be ignored.
1.
b
v
E
P
b
= 4
π ǫ
0
a
2
Q
2.
b
v
E
P
b
=
Q
4
π ǫ
0
a
3.
b
v
E
P
b
=
ǫ
0
Q A
4.
b
v
E
P
b
= 4
π ǫ
0
a Q
5.
b
v
E
P
b
=
ǫ
0
Q a
2
6.
b
v
E
P
b
= 2
ǫ
0
Q A
7.
b
v
E
P
b
=
Q
4
π ǫ
0
a
2
8.
b
v
E
P
b
=
Q
ǫ
0
A
9.
b
v
E
P
b
=
Q
2
ǫ
0
A
correct
Explanation:
Basic Concepts
Gauss’ Law, electrostatic
properties oF conductors.
Solution:
Consider the Gaussian surFace
shown in the fgure.
E
+
Q
E
S
Due to the symmetry oF the problem, there
is an electric ³ux only through the right and
leFt surFaces and these two are equal and
σ
=
Q
A
.
IF the cross section oF the surFace is
S
,
then Gauss’ Law states that
Φ
TOTAL
= 2
E S
=
1
ǫ
0
Q
A
S ,
since
Φ
TOTAL
≡
c
v
E
·
d
v
A,
so
E
=
Q
2
ǫ
0
A
.
002 (part 2 of 2) 10.0 points
Two uniFormly charged conducting plates are
parallel to each other. They each have area
A
. Plate #1 has a positive charge
Q
while
plate #2 has a charge
−
3
Q
.
+
Q
#1
−
3
Q
#2
P
x
y
Using the superposition principle fnd the
magnitude oF the electric feld at a point
P
in
the gap.
1.
b
v
E
P
b
=
Q
ǫ
0
2.
b
v
E
P
b
=
2
Q
ǫ
0
A
correct
3.
b
v
E
P
b
=
Q
3
ǫ
0
A
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2
4.
b
v
E
P
b
=
5
Q
ǫ
0
A
5.
b
v
E
P
b
=
3
Q
ǫ
0
A
6.
b
v
E
P
b
= 0
7.
b
v
E
P
b
=
3
Q
2
ǫ
0
A
8.
b
v
E
P
b
=
Q
2
ǫ
0
A
9.
b
v
E
P
b
=
4
Q
ǫ
0
A
10.
b
v
E
P
b
=
Q
ǫ
0
A
Explanation:
According to the result of part 1, the
electric Feld generated by plate #1 at P is
E
1
=
Q
2
ǫ
0
A
directed along the positive
x
axis.
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 Spring '00
 Littler
 Charge, Work, Electric charge

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