Transcript Powerpoint

Chapter 21
Electric Potential
Topics:
•
Electric energy
(Electric Potential Energy)
• Electric potential
• Gravitation Energy &
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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Electricity key concepts (Chs. 20 & 21) - Slide 1
General Concepts - These are always true
Electric Force and Field Model
• Charge Model
• E-field
• Definition
• E-field vectors
Fe, s®t
E=
qt
• E-field lines
å
Þ Fe, s®t = qE
Ex = E1x + E2 x + E3x + ×××
• Superposition E =
(note that for forces and fields,
we need to work in vector components)
net
x
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Electricity key concepts (Chs. 20 & 21) - Slide 2
General Concepts - These are always true
Energy, Electric Potential Energy, and Electric Potential
• Energy Definitions: KE, PEe, Peg, W, Esys, Eth and V
• Conservation of Energy
• Work by Conservative force = -- change of PE
• Electric Potential Energy and Electric Potential Energy
PEe
Ve =
qt
Þ
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PEe = qVe
Chapter 21 Key Equations (2)
Key Energy Equations from Physics 152
Work done by a conservative force (Fg, Fs, & Fe)
Also work done by conservative force
Wg = -DPEg is path independent
q1q2
PEe = k
r12
Electric Potential Energy for 2 point charges
(zero potential energy when charges an infinite distance apart)
elta Potential Energy for a uniform infinite plate
For one plate, zero potential energy is at infinity
For two plates, zero potential energy is at one plate or in
between the two plates
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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 elta V= 0 V is an equipotential line
(The electric force does zero work on a test charge that moves
on an equipotential line and elta PEe= 0 J)
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Slide 21-16
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)
Elta 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 in
between the two plates
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
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 elta V= 0 V is an equipotential line
(The electric force does zero work on a test charge that moves
on an equipotential line and elta PEe= 0 J)
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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
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Slide 21-25
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 elta V
• Higher potential as you approach a positive charge; lower potential as you
approach a negative charge
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Slide 21-16
Connecting Potential and Field
Slide 21-31
Checking Understanding
Rank in order, from largest to smallest, the electric
potentials at the numbered points.
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Slide 21-14
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.
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Slide 21-11
The Potential Inside a Parallel-Plate Capacitor
Uelec
Q
V=
= Ex =
x
q
Î0 A
Slide 21-25
Electric Potential of a Point Charge
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Slide 21-27
Electric Potential: Charged Sphere
Outside of a sphere of charge Q the potential has the same form as
for a point charge Q:
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Slide 21-28
Assembling a square of charges
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Slide 21-16
Analyzing a square of charges
Energy to Assemble
Wme = elta PEE = PEEf - PEEi
(PEEi = 0 J)
PEEf = q1Vnc@1 + q2V1@2 + q3V12@3 + q4V123@4
V123@4 = V1@4 +V2@4 + V3@4
Energy to move
(Move 2q from Corner to Center)
Wme = elta PEE = PEEf - PEEi
= q2qV123@center - q2qV123@corner
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Slide 21-16
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?
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Slide 21-16
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Slide 21-15
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.
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.
Slide 21-13
A Topographic Map
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. 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.Where could an electron be
placed so that it would not
move?
5. At which point is the magnitude of the electric field the greatest?
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