1
2
18.1 Electric Potential Energy
•
The electric force, like the
gravitational force, is a
conservative force.
(
Conservative
force: The work is pathindependent.
)
•
As in mechanics, work is
•
Work done on the positive
charge by moving it from A to B
A
B
E
!"
d
q
cos
Fd
W
=
qEd
Fd
W
=
=
q
cos
3
•
The work done by a conservative force equals
the
negative
of the change in potential energy,
D
PE
This equation is valid only for the case of a uniform electric
field
PE
W
qEd
D
=

=
If a charged particle moves
perpendicular to electric field lines,
no work is
done.
if d
^
E
4
•
The
potential difference
between points A and B, V
B
V
A
, is
defined as the change in potential energy (final minus initial
value) of a charge, q, moved from A to B, divided by the
charge
•
Electric potential is a scalar quantity
•
Electric potential difference is a measure of electric energy
per unit charge
•
Potential is often referred to as “voltage”
B
A
PE
V
V
V
q
D
D
=

=
If the work done by the electric field is zero, then the electric potential must
be constant
5
•
Electric potential difference is the work done to
move a charge from a point A to a point B
divided by the magnitude of the charge. Thus the
SI units of electric potential difference
•
In other words, 1 J of work is required to move a 1 C of charge
between two points that are at potential difference of 1 V
•
Question: How can a bird stand on a high voltage line without
getting zapped?
1
1
V
J C
=
6
•
Units of electric field (N/C) can be expressed in
terms of the units of potential (as volts per meter)
•
Because the positive tends to move in the direction of the
electric field, work must be done on the charge to move it in the
direction, opposite the field. Thus,
–
A positive charge gains electric potential energy when it is moved in a
direction opposite the electric field
–
A negative charge looses electrical potential energy when it moves in the
direction opposite the electric field
1
1
N C
V m
=
7
Analogy between electric and gravitational
fields
•
The same kineticpotential energy theorem works here
•
If a positive charge is released from A, it accelerates in the direction of
electric field, i.e. gains kinetic energy
•
If a negative charge is released from A, it accelerates in the direction
opposite the electric field
A
B
q
d
A
B
m
d
E
!"
g
!"
i
i
f
f
KE
PE
KE
PE
+
=
+
8
Example: motion of an electron
V
ab
What is the speed of an electron accelerated from
rest across a potential difference of 100V?
Given:
D
V=100 V
m
e
= 9.11
×
10
31
kg
m
p
= 1.67
×
10
27
kg
e = 1.60
×
10
19
C
Find:
v
e
=?
v
p
=?
s
m
v
s
m
v
m
V
q
v
V
q
mv
V
q
PE
KE
KE
PE
KE
PE
KE
p
e
f
f
i
f
f
f
i
i
/
10
3
.
1
/
10
9
.
5
2
2
1
5
6
2
´
=
´
=
D

=
D

=
D

=
D
=

+
=
+
9
18.2 Electric potential and potential energy due
to point charges
•
Electric circuits: point of zero potential is defined by grounding
some point in the circuit
•
Electric potential due to a point charge at a point in space:
point of zero potential is taken at an infinite distance from the
charge
•
With this choice, a potential can be found as
•
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 Spring '17
 hammed
 Electric Potential, Energy, Potential Energy, Electric charge, electric ﬁeld