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Introduced the concept of
electric field
E
to deal with
forces
Introduced
electric potential
V
to deal with
work
and
energy
Electric potential:
electric potential energy per unit charge
Potential Energy
Potential energy is associated with pairs of interacting objects
A
single particle
has
no
electric potential energy
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View Full Documentq
1
q
2
r
12
!
E
system
"
W
int
=
W
ext
Δ
U
el
≡

W
int
!
K
system
+
!
U
el
=
W
ext
+
Q
Total energy of the system can be changed (
only
) by external forces.
Work done by internal forces:
!
U
el
=
"
W
int
=
"
!
F
int
•
d
!
r
i
f
#
Electric Potential Energy of Two Particles
Energy of the system:
1.
Energy of particle
q
1
2.
Energy of particle
q
2
3.
Interaction energy
U
el
To change the energy of particles we have to perform work.
!
E
system
=
W
ext
+
W
int
+
Q
if
!
(
mc
2
)
=
0
:
The potential energy of a pair of particles is:
(joules)
12
2
1
0
4
1
r
q
q
U
el
!"
=
Electric Potential Energy
Each
(
i,j
)
pair interacts:
potential energy
U
ij
!
!
<
<
=
=
j
i
j
i
ij
j
i
ij
el
r
q
q
U
U
0
4
1
"#
The potential energy of multiple particles is:
U
el
> 0 for two likesign charges (
repulsion
)
U
el
< 0 for two unlikesign charges (
attraction
)
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View Full DocumentElectric potential
≡
electric potential energy per unit charge
q
U
V
el
=
Units:
J/C = V (Volt)
Electric potential – often called
potential
Electric potential difference – often called
voltage
Electric Potential
Volts per meter = Newtons per Coulomb
r
q
V
1
0
4
1
!"
=
r
→∞
, V=0
Negative charge
Positive charge
V
at Infinity
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View Full DocumentDefinitions:
q
F
E
!
!
=
q
U
V
el
=
Force = negative gradient of potential energy:
dx
dU
F
x
!
=
F
x
/
q
=
!
d U
/
q
( )
dx
dx
dV
E
x
!
=
Electric field is the negative gradient of potential:
x
V
E
x
!
!
"
=
y
V
E
y
!
!
"
=
z
V
E
z
!
!
"
=
Are units OK?
J/(C
.
m)=N
.
m/(C
.
m)=N/C
Electric Field and Potential