Transcript Today`s Powerpoint

Chapter 21
Electric Potential
Topics:
• Electric potential energy
• Electric potential
• Conservation of energy
Sample question:
Shown is the electric potential measured on the surface of a patient.
This potential is caused by electrical signals originating in the beating
heart. Why does the potential have this pattern, and what do these
measurements tell us about the heart’s condition?
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Slide 21-1
Chapter 21 Key Equations (Physics 151)
Key Energy Equations from Physics 151
Definition of Work
Work W = F i Dr = F Dr cos a
Where a = angle between the vectors
Work- Energy Theorem (only valid when particle model applies)
Wnet = DKE
Work done by a conservative force (Fg, Fs, & Fe)
Also work done by conservative force
Wg = -DPEg
is path independent
Conservation of Energy Equation
KEi +
å
PEi + D Esys = KE f +
different types
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å
PE f + DEth
different types
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Electric Potential Energy
Case A - Book starts & stops at rest
WNet = DEK = 0J
Whand + Wg = 0 Þ Whand = -Wg = DEg
Case C - Charge at rest at A and B
WNet = DEK = 0J
Whand + We = 0 Þ Whand = -We = DEe
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Slide 21-9
Chapter 21 Key Equations (2)
Key Energy Equations from Physics 152
q1q2
PEe = k
r12
Electric Potential Energy for 2 point charges
(zero potential energy when charges an infinite distance apart)
Potential Energy for a uniform infinite plate
DPEe = -We = - éë Fe × Dr cos a ùû = - ( q E ) Dr cos a
For one plate, zero potential energy is at infinity
For two plates, zero potential energy is at one plate or
inbetween the two plates
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Slide 21-16
Path Independence
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Slide 21-16
Changes in Electric Potential Energy ΔEe
Is the change ∆PEe of a + charged particle positive, negative,
or zero as it moves from i to f?
(a) Positive (b) Negative (c) Zero (d) Can’t tell
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Slide 21-11
Electric Potential
Uelec = qV; V = U elec / q
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Slide 21-10
Chapter 21 Key Equations (3)
Key Points about Electric Potential
Electric Potential is the Electric Potential Energy per Charge
PEe
V=
qtest
DPEe
We
DV =
=qtest
qtest
Electric Potential increases as you approach positive source
charges and decreases as you approach negative source
charges (source charges are the charges generating the electric
field)
A line where V= 0 V is an equipotential line
(The electric force does zero work on a test charge that moves
on an equipotential line and PEe= 0 J)
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Slide 21-16
Electric Potential and E-Field for Three Important Cases
For a point charge
q
1 q
V=K =
r 4pe 0 r
For very large charged plates, must use
DPEe
We
Fe i Dr
qtest E i Dr
DV =
==== -E i Dr = - E Dr cos a
qtest
qtest
qtest
qtest
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Slide 21-25
Checking Understanding
Rank in order, from largest to smallest, the electric
potentials at the numbered points.
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Slide 21-14
Example Problem
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.
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Slide 21-22
E-field lines and Equipotential lines
E-field Lines
• Go from + charges to - charges
• Perpendicular at surface of conductor or charged surface
• E-field in stronger where E-field lines are closer together
• More charge means more lines
Equipotential Lines
• Parallel to conducting surface
• Perpendicular to E-field lines
• Near a charged object, that charges influence is greater, then blends as
you to from one to the other
• E-field is stronger where Equipotential lines are closer together
• Spacing represents intervals of constant V
• Higher potential as you approach a positive charge; lower potential as you
approach a negative charge
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Slide 21-16
A Topographic Map
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Slide 21-12
Topographic Maps
1. Describe the region
represented by this map.
2. Describe the directions a
ball would roll if placed at
positions A – D.
3. If a ball were placed
at location D and
another ball were placed
at location C and both were
released,
which would have the greater acceleration?
Which has the greater potential energy when released?
Which will have a greater speed when at the bottom of the hill?
4. What factors does the speed at the bottom of the hill depend on? What factors
does the acceleration of the ball depend on?
5. Is it possible to have a zero acceleration, but a non-zero height? Is it possible
to have a zero height, but a non-zero acceleration?
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Slide 21-16
Equipotential Maps (Contour Maps)
1.Describe the charges that
could create equipotential lines
such as those shown above.
2.
2.Describe the forces a proton
would feel at locations A and B.
3. Describe the forces an
electron would feel at locations
A and B
4.
4.Where could an electron be
placed
that is
it would
not
5. At
whichsopoint
the magnitude
of the electric field the greatest?
move?
6. Is it possible to have a zero electric field, but a non-zero electric potential?
7. Is it possible to have a zero electric potential, but a non-zero electric field?
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Slide 21-16
3D view
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Slide 21-16
Connecting Potential and Field
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Slide 21-31
Reading Quiz
4. The electric field
A.
B.
C.
D.
is always perpendicular to an equipotential surface.
is always tangent to an equipotential surface.
always bisects an equipotential surface.
makes an angle to an equipotential surface that depends
on the amount of charge.
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Slide 21-12
Answer
4. The electric field
A.
B.
C.
D.
is always perpendicular to an equipotential surface.
is always tangent to an equipotential surface.
always bisects an equipotential surface.
makes an angle to an equipotential surface that depends
on the amount of charge.
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Slide 21-13
Example Problem
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?
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Slide 21-33
Graphical Representations of Electric Potential
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Slide 21-13
The Potential Inside a Parallel-Plate Capacitor
Uelec
Q
V=
= Ex =
x
q
Î0 A
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Slide 21-25
Electric Potential of a Point Charge
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Slide 21-27
Reading Quiz
3. The electric potential inside a parallel-plate capacitor
A.
B.
C.
D.
E.
is constant.
increases linearly from the negative to the positive plate.
decreases linearly from the negative to the positive plate.
decreases inversely with distance from the negative
plate.
decreases inversely with the square of the distance from
the negative plate.
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Slide 21-10
Answer
3. The electric potential inside a parallel-plate capacitor
A.
B.
C.
D.
E.
is constant.
increases linearly from the negative to the positive
plate.
decreases linearly from the negative to the positive plate.
decreases inversely with distance from the negative
plate.
decreases inversely with the square of the distance from
the negative plate.
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Slide 21-11