PHY2049 Fall 2010
Profs. S. Hershfield, A. Petkova
Exam 1 Solution
1. Four charges are placed at the corners of a rectangle as shown in the figure. If
Q
1
= 1
μ
C,
Q
2
=

2
μ
C,
Q
3
= 1
μC
, and
Q
4
= 2
μC
, what is the magnitude
of the net force on
Q
4
?
Answer:
11.4 N
Solution:
Make a table showing the components of each of the forces and then add the components.
F on 4 by 1
0

k
(1
μC
)(2
μC
)
/
(3
cm
)
2
F on 4 by 2
+0
.
8
k
(2
μC
)(2
μC
)
/
(5
cm
)
2
+0
.
6
k
(2
μC
)(2
μC
)
/
(5
cm
)
2
F on 4 by 3

k
(1
μC
)(2
μC
)
/
(4
cm
)
2
0
F total
0.27 N
11.36 N
The directions were obtained using opposite charges attract and like charges repel. The factors of 0.8 and 0.6 are the
trigonometric factors to determine the x and ycomponents. The magnitude of the force is
radicalBig
F
2
x
+
F
2
y
.
2. Five charges of magnitude
e
and sign indicated in the figure are placed on a
line.
The separation between the charges is
d
.
What is the magnitude and
direction of the force on the middle charge?
Answer:
1.5
ke
2
/d
2
, left
Solution:
For this problem again use opposite charges attract and like charges repel. Label the charges 1 to 5 from left
to right. As for the previous problem it is helpful to make a table:
F on 3 by 1
ke
2
/
(2
d
)
2
to the right
F on 3 by 2
ke
2
/
(
d
)
2
to the left
F on 3 by 4
ke
2
/
(
d
)
2
to the left
F on 3 by 5
ke
2
/
(2
d
)
2
to the right
F total
1.5
ke
2
/d
2
to the left
3. The following tests are made on an object
X
of unknown charge and material.
(i)
A positively charged object is attracted to X.
(ii)
A negatively charge object is attracted to X.
Which of the following are possible explanations of this behavior?
Answer:
X
is a neutral conductor.
Solution:
As demonstrated in class and also in the book (see Fig. 214), when a charged object is brought next to a
neutral conductor, there is an induced charge near the charged object. For example, a positive charge brought near a
neutral conductor will induce a negative charge near the surface of the conductor. The metal will be attracted to the
positive charge. The metal will also be attracted to a negative charge because induced charge in this case will be positive.
4. How many excess electrons are in

2
μC
charge?
Answer:
10
13
Solution:
The charge of an electron is

1
.
6
×
10

19
C
. (

2
×
10

6
C
)
/
(

1
.
6
×
10

19
C
)
≈
10
13
.
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5.
A
and
B
are identical conducting spheres. Sphere
A
is initially charged to 1 C, and sphere
B
has no charge initially. The
following five steps are done.
(i) Sphere
A
is touched to sphere
B
.
(ii) The spheres are separated and sphere
B
is grounded.
(iii) Sphere
A
is again touched to sphere
B
.
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 Fall '08
 Any
 Physics, Charge, Force, Electric charge, qenc, Qshell, A. Petkova

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