Electric Potential Energy
The electric potential energy of charge q in a uniform
electric field is
where s is measured from the negative plate and U0 is the
potential energy at the negative plate (s = 0). It will often
be convenient to choose U0 = 0, but the choice has no
physical consequences because it doesn t affect ΔUelec, the
change in the electric potential energy. Only the change is
significant.
Analogy to Gravitational PE
Gravitation PE depends on mass
General Physics 2
Electric potential energy depends
on charge
Electric Potential
2
The Potential Energy of Point Charges
Consider two point charges, q1 and q2, separated by a
distance r. The electric potential energy is
This is explicitly the energy of the system, not the energy of
just q1 or q2.
Note that the potential energy of two charged particles
approaches zero as r → ∞.
Which set has a positive potential energy?
Which set has a negative potential energy?
EXAMPLE 29.2 Approaching a charged sphere
EXAMPLE 29.2 Approaching a charged sphere
The Potential Energy of a Dipole
The potential energy of an electric dipole p in a uniform
electric field E is
The potential energy is minimum at ø = 0° where the dipole
is aligned with the electric field.
Remember p = qs
Electrical Potential Energy
•  For a charge in a uniform electric field
•  For point charges
Think-Pair-Share
•  What is the potential energy of this system,
taking U = 0 at a great distance?
+4Q
General Physics 2
Electric Potential
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Think-Pair-Share
•  What is the potential energy of this system,
taking U = 0 at a great distance?
General Physics 2
Electric Potential
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Workbook Problems on Electric Potential
Energy
•  P. 29-1 #1
•  P.29-3 #5, 6
•  P29-4 #7, 8
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The Electric Potential
We define the electric potential V (or, for brevity, just the
potential) as
Charge q is used as a probe to determine the electric
potential, but the value of V is independent of q. The
electric potential, like the electric field, is a property of
the source charges.
The unit of electric potential is the joule per coulomb,
which is called the volt V:
The Electric Potential of a Point Charge
Let q be the source charge, and let a second charge q', a
distance r away, probe the electric potential of q. The
potential energy of the two point charges is
By definition, the electric potential of charge q is
The potential extends through all of space, showing the
influence of charge q, but it weakens with distance as 1/r.
This expression for V assumes that we have chosen V = 0 to
be at r = ∞.
Equipotential Lines
•  connect points in space at same potential
•  equipotential surface is perpendicular to
electric field lines
General Physics 2
Electric Potential
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Electric Field & Equipotential Lines
•  Draw field lines and equipotential lines for
the following charge distributions
-
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Electric Potential
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Electric Field & Equipotential Lines
•  Draw field lines and equipotential lines for
the following charge distributions
+
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EXAMPLE 29.8 Calculating the potential of a
point charge
QUESTIONS: EXAMPLE 29.8 Calculating the potential of a
point charge
Plug & Chug
•  What is the electric potential 15.0 cm from a
4.00 x 10-6 C point charge?
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The Electric Potential of a Charged Sphere
In prac(ce, you are more likely to work with a charged sphere, of radius R and total charge Q, than with a point charge. Outside a uniformly charged sphere, the electric poten(al is iden(cal to that of a point charge Q at the center. That is, Or, in a more useful form, the poten(al outside a sphere that is charged to poten(al V0 is Plug & Chug
•  What is the electric potential 15.0 cm from a
charged sphere with a charge of 4.00 x 10-6 C
and a radius of 1.0 cm?
•  What is the electric potential 20.0 cm from a
1.0 cm diameter charged sphere that has been
charged to 1000V?
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The Electric Potential of Many Charges
The electric poten(al V at a point in space is the sum of the poten(als due to each charge: where ri is the distance from charge qi to the point in space where the poten(al is being calculated. In other words, the electric poten5al, like the electric field, obeys the principle of superposi5on. EXAMPLE 29.10 The potential of two charges
QUESTION: EXAMPLE 29.10 The potential of two charges
The Electric Potential Inside a Parallel-Plate
Capacitor
The electric potential inside a parallel-plate capacitor is
where s is the distance from the negative electrode.
The electric potential, like the electric field, exists at all
points inside the capacitor.
The electric potential is created by the source charges on
the capacitor plates and exists whether or not charge q is
inside the capacitor.
Electric Potential
Think of analogy with
gravitational PE, where
object with positive PE will
fall if released.
Here, p+ has high PE
when near + plate and will
fall toward negative plate
when released
Think of + charge when
wondering if something is
high or low potential
+ charges
move from
high to low
potential
Electric Potential
low PE
High PE
-
-
Unlike mass, charge can
be + or -. Thus, PE depends
on the sign of the charge.
For example, an e- will have
high PE when near the
-  plate and will fall toward
the + plate when released
- charges
move from
low to high
potential
EXAMPLE 29.7 A proton in a capacitor
QUESTIONS:
EXAMPLE 29.7 A proton in a capacitor
EXAMPLE 29.7 A proton in a capacitor
EXAMPLE 29.7 A proton in a capacitor
EXAMPLE 29.7 A proton in a capacitor
EXAMPLE 29.7 A proton in a capacitor
!
Electrostatic Potential & PE
•  When dealing with discrete point charges:
! kq1q2
F = 2 rˆ
r
! kq
E = 2 rˆ
r
kq1q2
U=
r
kq
V=
r
!
U and V are scalars
General Physics 2
F and E are vectors
Electric Potential
!
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Workbook
•
•
•
•
•
P29-6 #11, 13
P29-7 #15
P29-9 #17, 18
P29-10 #20
P29-11 #22
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