gilbert (amg3448) – HW01 – tsoi – (57210)
1
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printout
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have
30
questions.
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before answering.
001
10.0 points
A circular ring made of an insulating material
is cut in half.
One half is given a charge

q
uniformly distributed along its arc.
The
other half is given a charge +
q
also uniformly
distributed along its arc. The two halves are
then rejoined with insulation at the junctions
J
, as shown.
x
y

q
+
q
J
J


















+
+
+
+
+
+
+
+
++
+
+
+
+
+
+
+
+
q
e
If there is no change in the charge distri
butions, what is the direction of the net elec
trostatic force on an electron located at the
center of the circle?
1.
Toward the top of the page
2.
To the right
3.
Toward the bottom of the page
correct
4.
Into the page
5.
To the left
Explanation:
The rejoined system is symmetrical about
the diameter perpendicular to the line con
necting two junctions. The electrostatic force
is along the direction connecting the two
charges (repulsive for charges of the same
sign and attractive for charges of the oppo
site sign), so the force on the electron is paral
lel to the symmetrical axis and points toward
the positive charge;
i.e.
, toward the bottom of
the page.
002
10.0 points
A strong lightning bolt transfers about 26 C
to Earth.
How many electrons are transferred?
The
charge on an electron is

1
.
60218
×
10

19
C.
Correct answer: 1
.
62279
×
10
20
.
Explanation:
Let :
q
= 26 C
and
q
e
=

1
.
60218
×
10

19
C
.
The charge is proportional to the number
of electrons, so
q
=
n

q
e

n
=
q

q
e

=
26 C


1
.
60218
×
10

19
C

=
1
.
62279
×
10
20
.
003
10.0 points
A particle with charge 5
μ
C is located on
the
x
axis at the point

4 cm
,
and a second
particle with charge

3
μ
C is placed on the
x
axis at

8 cm
.
The
Coulomb
constant
is
8
.
9875
×
10
9
N
·
m
2
/
C
2
.
2
4
6
8
10

2

4

6

8

10
5
μ
C

3
μ
C
3
μ
C
x
→
(cm)
What is the magnitude of the total elec
trostatic force on a third particle with charge
3
μ
C placed on the
x
axis at 2 cm ?
Correct answer: 29
.
3592 N.
Explanation:
Let :
q
1
= 5
μ
C = 5
×
10

6
C
,
q
2
=

3
μ
C =

3
×
10

6
C
,
q
3
= 3
μ
C = 3
×
10

6
C
,
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gilbert (amg3448) – HW01 – tsoi – (57210)
2
x
1
=

4 cm =

0
.
04 m
,
x
2
=

8 cm =

0
.
08 m
,
and
x
3
= 2 cm = 0
.
02 m
.
Coulomb’s law (in vector form) for the elec
tric force exerted by a charge
q
1
on a second
charge
q
3
, written
F
13
is
F
13
=
k
e
q
1
q
3
r
2
ˆ
r
13
,
where ˆ
r
13
is a unit vector directed from
q
1
to
q
3
;
i.e.
,
r
13
=
r
3

r
1
.
x
13
=
x
3

x
1
= (2 cm)

(

4 cm) = 0
.
06 m
x
23
=
x
3

x
2
= (2 cm)

(

8 cm) = 0
.
1 m
ˆ
x
13
=
x
3

x
1
(
x
3

x
1
)
2
= +ˆ
ı
ˆ
x
23
=
x
3

x
2
(
x
3

x
2
)
2
= +ˆ
ı
Since the forces are collinear, the force on the
third particle is the algebraic sum of the forces
between the first and third and the second and
third particles.
F
=
F
13
+
F
23
=
k
e
q
1
r
2
13
ˆ
r
13
+
q
2
r
2
23
ˆ
r
23
q
3
= 8
.
9875
×
10
9
N
·
m
2
/
C
2
×
(5
×
10

6
C)
(0
.
06 m)
2
(+ˆ
ı
)
+
(

3
×
10

6
C)
(0
.
1 m)
2
(+ˆ
ı
)
×
(3
×
10

6
C)
= 37
.
4479 N + (

8
.
08875 N)
= 29
.
3592 N
,
with a magnitude of
29
.
3592 N
.
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 Spring '10
 TSOI
 Physics, Charge, Electric charge

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