CHAPTER
19
ELECTRIC POTENTIAL ENERGY
AND THE ELECTRIC POTENTIAL
CONCEPTUAL QUESTIONS
_____________________________________________________________________________________________
1.
REASONING AND SOLUTION
The work done in moving a charge
q
0
from A to B is given by
Equation 19.4:
W
AB
=
q
0
(
V
A

V
B
)
.
For the cases in the drawing, we have
Case 1:
W
AB
=
q
0
(150 V

100 V)
=
q
0
(50 V)
Case 2:
W
AB
=
q
0
[25 V

(–25 V )]
=
q
0
(50 V)
Case 3:
W
AB
=
q
0
[–10 V

(–60 V )]
=
q
0
(50 V)
The work done on the charge by the electric force is the same in each case.
_____________________________________________________________________________________________
2
.
REASONING AND SOLUTION
The potential at a point in space that is a distance
r
from a point
charge
q
is given by Equation 19.6:
V
=
kq
/
r
.
When more than one point charge is present, the
total potential at any location is the algebraic sum of the individual potentials created by each charge
at that location.
A positive point charge and a negative
point charge have equal magnitudes.
One
of the charges is fixed to one corner of a
square.
If the other charge is placed
opposite to the first charge along the
diagonal of the square, then each charge
will be the same distance
L
from the
empty corners.
The potential at each of
the empty corners will be
V
=
k
(
+
Q
)
L
+
k
(

Q
)
L
=
0
q
=
+Q
q
=
– Q
L
L
L
L
Therefore, if the potential at each empty corner is to be the same, then the charges must be placed at
diagonally opposite corners as shown in the figure.
_____________________________________________________________________________________________
3
.
REASONING AND SOLUTION
The potential at a point in space that is a distance
r
from a point
charge
q
is given by Equation 19.6:
V
=
kq
/
r
.
When more than one point charge is present, the total
potential at any location is the algebraic sum of the individual potentials created by each charge at
that location.
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ELECTRIC POTENTIAL ENERGY AND THE ELECTRIC POTENTIAL
Three point charges have identical
magnitudes, but two of the charges are
positive and one is negative.
These
charges are fixed to the corners of a
square, one to a corner, as shown in the
figure.
The potential at the empty corner is
given by
V
=
q
1
L
+
q
2
L
2
+
q
3
L
L
L
q
3
q
1
q
2
L
2
Using
q
to denote the magnitude of each charge, we have the following possibilities:
q
1
and
q
2
are positive:
V
=
kq
L
+
kq
L
2

kq
L
=
kq
L
2
q
1
and
q
3
are positive:
V
=
kq
L

kq
L
2
+
kq
L
=
kq
L
2

1
2
q
2
and
q
3
are positive:
V
= 
kq
L
+
kq
L
2
+
kq
L
=
kq
L
2
In each case, the potential at the empty corner is positive.
_____________________________________________________________________________________________
4
.
REASONING AND SOLUTION
Four
point charges of equal magnitude are
placed at the corners of a square as shown
in the figure at the right.
The electric field at the center of the
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 Spring '08
 Akgun
 Physics, Proton, Charge, Electric Potential, Energy, Potential Energy, Work, Electric charge, Electric potential energy

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