saldana (avs387) – homework 02 – Turner – (56705)
1
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printout
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13
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001
10.0 points
Four
point
charges,
each
of
magnitude
11
.
28
μ
C, are placed at the corners of a square
58
.
5 cm on a side.
If
three
of
the
charges
are
positive
and
one
is
negative,
find
the
magnitude
of
the
force
experienced
by
the
negative
charge.
The value of Coulomb’s constant is
8
.
98755
×
10
9
N
·
m
2
/
C
2
.
Correct answer: 6
.
39644 N.
Explanation:
Let :
k
e
= 8
.
98755
×
10
9
N
·
m
2
/
C
2
,
d
= 58
.
5 cm = 0
.
585 m
,
and
Q
= 11
.
28
μ
C = 1
.
128
×
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
.
128
×
10

5
C
)
2
(0
.
585 m)
2
= 3
.
34155 N
,
and
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
(3
.
34155 N) =
6
.
39644 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.
Use 2
π R
for the distance.
2.
None of these
3.
Use 2
R
for the distance.
4.
The result of the calculation is zero.
cor
rect
5.
Use
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

2
.
40
×
10

9
C are separated by a distance
of 45
.
0 cm.
Find the equilibrium position for a third
charge of +19
.
0
×
10

9
C by identifying its
distance from
q
1
.
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 Spring '10
 Turner
 Charge, Work, Correct Answer, Electric charge, Saldaña

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