Electric Potential Energy &
Electric Potential
Honors Physics
Mr. Kuffer
We Know… Coulomb’s Law
Q1
r
Q2
If either Q1 or Q2 increases the Force increases
If either Q1 or Q2 decreases the Force decreases
If r, the distance between the two charges, increases
the force decreases
If r, the distance between the two charges, decreases
the force increases
Because r appears as 1/r2 the dependence on r is
strong
We know… Coulomb’s Law
Q1
r
Q2
Double r. F decreases by a factor of 4
If r -> r/3 F increases by a factor of 9
If r decreases to ¼ of its value,
F becomes 16 times as large
We know… The Electric Field
The electric field is the force on a
small charge, divided by the charge:
Fields play an intermediate role in the force between bodies.
We treat fields as a property of space. Charges create fields.
Given the field we can calculate the forces on ANY charged
objects
Field Lines
The electric field between two
closely spaced, oppositely
charged parallel plates is
constant.
Today’s Topics
• Electric Potential Energy
• Electric Potential
• Electric Equi-potential Lines
Recall… Work
• You do work when you push an object up a hill
• The longer the hill the more work you do: more
distance
• The taller the hill, the more work you do: more force
The work, W, done on an object by an agent
exerting a constant force is the product of the
component of the force in the direction of the
displacement and the magnitude of the
displacement
W  F||d
Energy is capacity to do work
note Ep aka UG
• Gravitational Potential Energy U G  mgh
• Kinetic Energy
• Energy can be converted into other forms of
1
K  mv
energy
2
• When we do work on any object we transfer
energy to it
  U G
• Energy cannot be created or destroyed
2
W  K  U G
Potential Energy
Ug doing work!!
Ue doing work!!
The presence of charges can give rise to a
potential energy (PE)
Potential Energy
We determined the
potential energy Uel of a
spring by asking how
much work we do to
compress it.
We can determine the
potential energy of a
charge distribution by
how much work we do to
bring the charge to its
position
Potential of a Parallel-Plate Capacitor
Slide 21-24
Potential Energy
• High Gravitational PE.
Ball will roll down hill
• High Electrical Potential Energy
• Positive charge will move away
• Positive charge will “fall” from high
• potential energy to low PE
+
• Negative charge “falls” from high PE to
• low PE
•
-
Electric Potential Energy
charges also have electrical potential energy
W  Fd
+Q
E
 q 0 Ed
F  q 0E
d
U e  q0 Ed
+Q
Note the loss in
potential Energy.
Hence the ‘-’ sign
v
Electric Potential Energy
• Work done (by electric field) on
charged particle is qEd
• Particle has gained Kinetic Energy (qEd)
• Particle must therefore have lost
Potential Energy U=-qEd
Electrostatic Potential Energy
Change in electric
potential energy is work
done against electric
force (from b to a):
PEa – PEb = qEd
a---
Compare Ug
b---
Ug = mg (a-b) =mgh
Electric Potential
(Not Electric Potential Energy)
• Just as Electric field depends on space and
allows us to compute force on any charge,
Electric Potential depends on space and allows
us to calculate Uelec for any charge.
Electric Potential
compare with the Electric Field and Coulomb Force
U
V 
q0
F
E
q0
U  q 0 V
F  q 0E
If we know the potential field this allows us to
calculate changes in potential energy for any
charge introduced
Electrostatic Potential Energy and Potential
Difference
Electric potential is defined as potential energy per
unit charge:
U elec
V 
q
U elec  qV
Unit of electric potential: the volt (V).
1 V = I J/C.
Greater at B, Greater yet at C
Ue= qV
Ue= q V
Ue(B) = 10 nC * 400V
Electrostatic Potential Energy and Potential
Difference
Analogy between gravitational and electrical potential
energy:
A
A and B are the
same distance
from sphere
B
Which has higher potential energy
A, B or C the same?
A
A and B are the
same distance
from sphere
B
Which has higher potential energy
A, B or C the same?
A
A and B are the
same distance
from sphere
B
Which is at a higher potential (voltage)
A,B or C the same?
A
A and B are the
same distance
from sphere
B
Careful here!
Potential is a
measure per
individual charge!
Which is at a higher potential (voltage)
A,B or C the same?
(electric potential is a "property" related only to the electric field itself)
Electrostatic Potential Energy and Potential
Difference
Only changes in potential can be measured, allowing
free assignment of V = 0… where there is no change
there is no potential difference.
Vba = Vb – Va = Ue(b) –Ue (a)
q
Therefore Potential (V) is unaffected by position change within
equipotential surfaces!
For Potential Difference… defining ‘zero’ is arbitrary… just like choosing a
frame of reference for Ug
Electric Potential
Electric Potential is a scalar
it is defined everywhere
it doesn’t depend on a charge being there
but it does not have any direction
Super Fun Review
Challenge!
Is the change in Ue ΔU,
A) positive
B) negative
C) zero
as a positive charge moves from point labeled i
to f?
+
i
f
Is the change in Ue ΔU,
A) positive
B) negative
C) zero
as a positive charge moves from point labeled i
to f?
+
i
f
Is the change in Ue ΔU,
A) positive
B) negative
C) zero
as a negative charge moves from point labeled i
to f?
+
i
f
Is the change in Ue ΔU,
A) positive
B) negative
C) zero
as a negative charge moves from point labeled i
to f?
+
i
f
Is the change in Ue ΔU,
A) positive
B) negative
C) zero
as a positive charge moves from point labeled i
to f?
+
i
f
Is the change in Ue ΔU,
A) positive
B) negative
C) zero
as a positive charge moves from point labeled i
to f?
+
i
f
Conceptual Example Problem
Note: q1, q2, & q3 are
positive test charges
The correct order of electrical potentials
from largest to smallest is
A) V1>V2>V3
B) V1=V2> V3
C) V1=V2 =V3
D) V3>V2=V1
E) V3>V2>V1
Slide 21-17
Conceptual Example Problem
Note:1 and 2 share an
equipotential surface.
The correct order of electrical potentials
from largest to smallest is
A) V1>V2>V3
B) V1=V2> V3
C) V1=V2 =V3
D) V3>V2=V1
E) V3>V2>V1
Slide 21-17
Conceptual Example Problem
The correct order of electrical potentials
from largest to smallest is
A) V1>V2>V3
B) V1=V2> V3
Note: q , q , & q are
positive test charges
C) V1=V2 =V3
D) V3>V2=V1
E) V3>V2>V1
1
2
3
Slide 21-17
Conceptual Example Problem
The correct order of electrical potentials
from largest to smallest is
A) V1>V2>V3
B) V1=V2> V3
Note: We are asked about
the Electric Potential… not
C) V1=V2 =V3
the Force the charge Feels!
D) V3>V2=V1
E) V3>V2>V1
Slide 21-17
Energy Conservation in Electric
Potentials
• Just as for mechanical systems Energy is
conserved. We can change potential energy to
kinetic energy and vice versa.
• Kf + qVf = Ki + qVi
• Kf –Ki = qVi –q Vf =-q(Vf –Vi)
ΔK = -qΔV
The more Potential is lost… the more Kinetic is gained
Charged Particle Moving Through a Potential
Difference
ΔK = -qΔV
Slide 21-18
Charged Particle Moving Through a Potential Difference
Be careful! Things are reversed for negative charge.
Negative charge speeds up if it moves
from region of lower to higher potential: ΔK = -qΔV
Slide 21-18
The Electron Volt, a Unit of Energy
One electron volt (eV) is the energy (not charge)
gained by an electron moving through a potential
difference of one volt.
Slide 21-19
Example Problem
A proton has a speed of 3.5 x 105 m/s at a point where the electrical
potential is 600 V. It moves through a point where the electric potential
is 1000 V. What is its speed at this second point?
Slide 21-20