Electric Potential
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•
As with mechanics, energy is a useful quantity in
studying electric forces
electric potential or potential
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•
electric potential energy per unit charge
potential difference, Φ
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•
•
only difference in potential energy is meaningful
Ve is the electrostatic potential energy relative to some
reference point
Volt: 1 V = 1 J/C
e
General Physics 2
V
kQ
 
q rPC
Electric Potential
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Analogy to Gravitational PE
Gravitation PE depends on mass
Electric potential energy depends
on charge
Φb
General Physics 2
Electric Potential
Φab
Φa
2
Electric Potential of Point Charge
•
Set V=0 at a distance of infinity
General Physics 2
Electric Potential
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Electric Potential of Multiple Charged Objects
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Superposition principle
  1   2  3  ...  N
N
kq1 kq2 kq3
kqN
kqi



 ...

rP1 rP 2 rP 3
rPN i1 rPi
General Physics 2
Electric Potential
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Electric Potential
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Electric Potential
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Equipotential Lines
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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
-
General Physics 2
Electric Potential
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Electric Field & Equipotential Lines
•
Draw field lines and equipotential lines for the
following charge distributions
+
General Physics 2
Electric Potential
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Relating Electric Field to Potential
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The change in electrical potential for a
small displacement in a static electric field
r r
d   E  dr
E x x, y,z  x

 

E x, y,z  E y x, y,z  y



E
x,
y,z


 z

 z
 
General Physics 2
Electric Potential
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Electrostatic Potential & PE
•
When dealing with discrete point charges:
kq1q2
Ve 
r
kq

r
Ve and Φ are scalars
General Physics 2
F and E are vectors
Electric Potential
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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
Capacitance
•
a capacitor stores electric charge
General Physics 2
Capacitors
13
Properties of Capacitors
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Capacitance, C
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Q=CV
Farad (F) = Coulomb / Volt
C depends on size, shape, relative position of
parallel plates (and material that separates
them)
permittivity of
free space =
2/(N m2)
8.85 General
x 10-12
C
Physics 2
surface area
per plate
Capacitors
separation
between plates
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Electron Volt, a Unit of Energy
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electron volt (eV)
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Joule is very large for dealing w/electrons, atoms
and molecules
eV is energy required to move 1 e- through a
potential difference of 1V
1 eV = qe V = (1.6 x 10-19 C)(1.0 V)
1 eV = 1.6 x 10-19 J
General Physics 2
Electric Potential
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Sign of Electric PE
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PE = 0 at infinity
Did you have to do work to bring charges from
infinity?
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yes -> charges have positive PE
Example:
-
•
-
no -> charges have negative PE
Example:
-
General Physics 2
+
Electric Potential
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ConcepTest
1.
2.
3.
positive
negative
zero
ConcepTest
Plug & Chug
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How much work does the electric field do in
moving a -7.7C charge from the ground to a
point whose potential is +55 V higher?
General Physics 2
Electric Potential
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Think-Pair-Share
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How much kinetic energy will an electron gain (in
joules and eV) if it accelerates through a potential
difference of 23,000 V in a TV picture tube?
What is its final velocity?
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Electric Potential
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Electric Potential & Electric Field
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For a uniform electric field
uniform electric
field
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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
-
General Physics 2
-
Electric Potential
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Which set has a positive potential energy?
Which set has a negative potential energy?
Plug & Chug
•
What is the electric potential 15.0 cm from a
4.00 x 10-6 C point charge?
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Electric Potential
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Think-Pair-Share
•
What is the potential at point A, taking V=0 at
a great distance?
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Electric Potential
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