terry (ect328) – homework 02 – Turner – (59130)
1
This
printout
should
have
13
questions.
Multiplechoice questions may continue on
the next column or page – find all choices
before answering.
001
10.0 points
Four
point
charges,
each
of
magnitude
13
.
5
μ
C, are placed at the corners of a square
63
.
5 cm on a side.
The
value
of
Coulomb’s
constant
is
8
.
98755
×
10
9
N
·
m
2
/
C
2
.
If three of the charges are positive and one
is negative, find the magnitude of the force
experienced by the negative charge.
Correct answer: 7
.
77592 N.
Explanation:
Let :
k
e
= 8
.
98755
×
10
9
N
·
m
2
/
C
2
,
d
= 63
.
5 cm = 0
.
635 m
,
and
Q
= 13
.
5
μ
C = 1
.
35
×
10

5
C
.
F
24
F
34
F
14
+
3
+
1
+
2

4
The forces are
F
34
=
F
24
=
k
e
Q
2
d
2
=
(
8
.
98755
×
10
9
N
·
m
2
/
C
2
)
×
(
1
.
35
×
10

5
C
)
2
(0
.
635 m)
2
= 4
.
0622 N
F
14
=
k
e
Q
2
(
√
2
d
)
2
=
1
2
k
e
Q
2
d
2
=
1
2
F
34
The vector sum of
F
24
and
F
34
is in the same
direction as
F
14
, so
F
=
F
14
+
radicalBig
F
34
2
+
F
24
2
=
1
2
F
34
+
radicalBig
2
F
34
2
=
parenleftbigg
1
2
+
√
2
parenrightbigg
F
34
=
parenleftbigg
1
2
+
√
2
parenrightbigg
(4
.
0622 N)
=
7
.
77592 N
.
002
10.0 points
A charge
Q
is spread uniformly along the
circumference of a circle of radius
R
. A point
charge
q
is placed at the center of this circle.
What is the total force exerted on
q
as
calculated by Coulomb’s law?
1.
The result of the calculation is zero.
cor
rect
2.
Use
R
for the distance.
3.
Use 2
π R
for the distance.
4.
None of these.
5.
Use 2
R
for the distance.
Explanation:
By symmetry and using the fact that the
charge is uniformly distributed along the cir
cumference, the total force on
q
is zero. For
example, consider a small element of charge
δQ
on the circle. The force on
q
is along the
vector connecting
δQ
and
q
.
But on the ex
act opposite side there is another element of
charge
δQ
which exerts an equal but opposite
force on
q
. This is true for every point on the
circle, so the net force is zero.
003
10.0 points
A charge
q
1
of

5
.
00
×
10

9
C and a charge
q
2
of

1
.
90
×
10

9
C are separated by a distance
of 35
.
0 cm.
Find the equilibrium position for a third
charge of +14
.
0
×
10

9
C by identifying its
distance from
q
1
.
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 Fall '09
 Turner
 Charge, Electric charge, Terry

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