Download Lecture-Electric Potential

11/3/2011
Potential Energy
• Gravitational
Potential
Energy
Electric Potential
Increases as you
move farther
from Earth
Physics 122
Eyres
Gravitational
i
U
K
increases
U changes as
you change r
Uf
f
K
U
U=0
Electrical
U changes as
you change r
=
i
+
Ui
U=0
f
+
K
K
Earth
=
Electrical
U changes as
you change r
=
i
Udecreases
-
K
U
increases
U
U=0
f
-
K
U
Uf
=
i
-
Ui
U=0
f
-
K
K
Udecreases
U
Ui
Ui
Uf
Increases or
decreases as you
move farther
from the charge
Electrical Potential Energy-signs
Electrical
= mgh
• Electrical
Potential
Energy
Increases as you
increase spring
extension/comp
ression
= 12 Δ 2
= mgh
Potential Energy
U increases as
you get
farther from
Earth
• Spring
Potential
Energy
+
Uf
+
-
=
Exercise
Is the change ∆U of the particle positive, negative,
or zero as it moves from i to f?
Exercise
Is the change ∆U of the particle positive, negative,
or zero as it moves from i to f?
HINT:
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
=
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
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11/3/2011
Electric Potential
=
=
!
!
!
!
#
−
%
#
−
%
=
&'() '*+ &'() '*+
!
=
-
,-
−
!
#
,.
!
%
= "!
#
−
Δ
%
= "# −"% !
= Δ"!
A Topographic Map
Checking Understanding
Rank in order, from largest to smallest, the electric
potentials at the numbered points.
HINT: / =
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Graphical Representations of Electric Potential
Δ
= Δ"!
−Δ0 = Δ"!
Δ
Can you link
all three
equations?
= Δ"!
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
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11/3/2011
Example
Example (How is this similar to the previous problem?)
105
m/s at a point where the
A proton has a speed of 3.5 x
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?
A proton is released from rest at point a. It then travels past point
b. What is its speed at point b?
Its about Energy! How do
you know?
Its about Energy! How do
you know?
Δ
Δ
Δ"!
Δ"!
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
The Potential Inside a Parallel-Plate Capacitor
Example: (How is this similar to the previous problems?)
A parallel-plate capacitor is held at a potential difference of 250 V.
A proton is fired toward a small hole in the negative plate with a
speed of 3.0 x 105 m/s. What is its speed when it emerges
through the hole in the positive plate? (Hint: The electric potential
outside of a parallel-plate capacitor is zero).
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
123 4
Δ"
Δ
Slope = E
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Example
Connecting Potential and Field
For the situation shown in the figure, find
A. The potential at points a and b.The potential difference
between a and b.
B. The potential energy of a proton at a and b.
C. The speed at point b of a proton that was moving to the right at
point a with a speed of 4.0 x 105 m/s.
D. The speed at point a of a proton that was moving to the left at
point b with a speed of 4.0 x 105 m/s.
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
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11/3/2011
Potential and Field for Three Important Cases
Example
Source charges create the
electric potential shown.
A. What is the potential at point
A? At which point, A, B, or C,
does the electric field have its
largest magnitude?
B. Is the magnitude of the
electric field at A greater than,
equal to, or less than at point
D?
C. What is the approximate magnitude of the electric field
at point C?
D. What is the approximate direction of the electric field at
point C?
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
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