Videos
SP212
Plasma Ball
http://youtu.be/2gttW4F86Sg
Plasma Demo with CFL
2nd day of lecture
Candle Flame (Lead in with this)
http://www.youtube.com/watch?v=a7_8Gc_Llr8
Ch. 24 – Electric Potential
Maj Jeremy Best USMC
Physics Department, U.S. Naval Academy
February 23, 2016
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
February 23, 2016
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Find the Physics: Potential
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
February 23, 2016
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The Electric Field
Two or more charged particles have electrostatic
forces between them, we have gone over this many
times so far.
The electric field is directly tied to the force exerted
on a charged particle by another charge: ~E = ~F/q.
We also talked about how two charges, (a dipole)
have potential energy.
This represents the potential Army vs. Navy Tug of war
Potential Energy being used
to exert our will on the
to do work to defeat Army.
enemy.
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
February 23, 2016
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U = −~p • ~E
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
February 23, 2016
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Electric Potential
Electric Potential
The concepts of work and energy allow us to get away
from the vector notation and all of the vector math .
The electric potential is defined as the work required
to transfer a unit of electric charge from an infinite
distance to a given point through an electric field . A
measure of the work required by an electric field to move
electric charges.
V =
U
q
Just as with potential energy in SP211, it is only
changes in electric potential that matter.
∆V = Vf − Vi =
∆U
q
∆V = Vf − Vi =
−W
q
and
Which is a scalar, not a vector.
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
February 23, 2016
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SI Potential
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Electric Potential and Energy
1 Volt = 1 Joule per Coulomb.
The SI unit for electric potential is the volt
(1 V = 1 J/C).
N
N
V
J
V
1 =
=1
C
C
J/C
N ·m
m
Finally, the Volt lets us define a more useful unit of
energy for use on these scales. The electron-volt is the
amount of energy required to move a single elementary
charge through a potential difference of one volt.
1 eV = 1.602 × 10−19 J
This unit conversion lets us rewrite the unit for the
electric field into a more useful form: V/m.
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
February 23, 2016
It is NOT potential, it is an amount of energy .
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Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
February 23, 2016
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More with Potential and Work
Equipotential Surfaces
An Equipotential Surface is a surface that is all at the
same potential. Charges may move along equipotential
surfaces without the field doing any work on them .
Electric potential is defined as the change in potential
energy per unit charge. But this is connected to the
work done on a particle:
∆U = Wapp → ∆V =
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
Wapp
−Wfield
=
q
q
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Equipotentials
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
February 23, 2016
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Electric Potential and the Field
For two chapters, we focused on the electric field, now
we’re talking about potential. How are they connected?
The electric field is connected to the force on a charged
particle, the potential is connected to the energy of the
particle .
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
February 23, 2016
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Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
February 23, 2016
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Electric Potential and the Field
Potential Energy
Recall the definition of the work done by a force:
Z f
~F · d~s
W =
i
Z ~
W
F
=
· d~s
q
q
Z f
~E · d~s
Vf − Vi = −
Zi f
~E · d~s
and if Vi = 0, V = −
All ships have some sort of
battery arrays. Submarines
How many volts of potential store very large battery
are here?
arrays low in the keel.
i
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
February 23, 2016
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The Potential Due to a Point Charge
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The Potential Due to a Point Charge
We begin our integration at a distance
R from a point charge q and move out
to ∞.
Z ∞
0
~E · d~s
V
f − Vi = −
Z ∞R
Vi =
E ds
R
Z ∞
1 q
=
ds
2
R 4π0 s
∞
−q
1
=
4π0 s R
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
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We conclude that
V =
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
1 q
4π0 r
February 23, 2016
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Potential Due to Multiple Point Charges
The Potential Due to a Dipole
The potential of many charges add up, just like electric
fields
V =
n
X
i=1
n
1 X qi
Vi =
4π0
ri
i=1
But this is only a straight algebraic sum, no components!
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
February 23, 2016
17 / 24
The Potential Due to a Dipole
The potential due to a dipole is easy,
since there are no components:
V = V(+) + V(−)
1
q
−q
=
+
4π0 r(+) r(−)
q r(−) − r(+)
=
4π0 r(−) r(+)
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
February 23, 2016
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V of a Continuous Charge Distribution
Same game we played with the electric field:
Z
Z
1
dq
V = dV =
4π0
r
If d is very small, and we are far away,
we can make this prettier
r(−) − r(+) ≈ d cos θ and r(−) r(+) ≈ r 2
q d cos θ
1 p cos θ
V =
=
4π0 r 2
4π0 r 2
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
February 23, 2016
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Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
February 23, 2016
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Getting the Field from the Potential
Potential Energy of a System of Charges
Since the potential is the integral of the field, the field
must be the derivative of the potential. Well, sort of.
Remember that the field is a vector, while the potential
is a scalar. What operator do you know that turns a
scalar into a vector?
Ex =
−∂V
∂x
~E = −∇V
−∂V
Ey =
∂y
Ez =
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
U =W
= qV
1 q1 q2
=
4π0 r
−∂V
∂z
February 23, 2016
A collection of charges has potential energy , because if
we leave them alone, they will start moving. That kinetic
energy has to come from somewhere. The potential
energy is
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Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
February 23, 2016
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Conductors are Equipotentials
Remember our definition of a potential difference:
Z f
~E · d~s
Vf − Vi = −
Wiley Plus Homework
Chapter 24: Questions 1, 2, 7, 12. Problems: 3, 4, 8, 16,
21, 24, 26, 28, 37, 44, 49, 102.
i
Vf − Vi = 0
Vf = Vi
Maj Jeremy Best USMC (Physics Department, U.S. Naval Academy)
SP212
February 23, 2016
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SP212
February 23, 2016
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