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
The Potential Inside a Parallel-Plate Capacitor
Uelec
Q
V=
= Ex =
x
q
Î0 A
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Slide 21-25
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
Dielectrics and Capacitors
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Dielectrics and Capacitors
The molecules in a dielectric tend to become oriented in a way that
reduces the external field.
This means that the electric field within the dielectric is
less than it would be in air, allowing more charge to be
stored for the same potential.
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Dielectric Constant
With a dielectric between its
plates, the capacitance of a
parallel-plate capacitor is
increased by a factor of the
dielectric constant κ:
=
ke 0
Dielectric strength is the maximum
field a dielectric can experience
without breaking down.
E0
E'=
k
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Storage of Electric Energy
The energy density, defined as the energy per unit
volume, is the same no matter the origin of the
electric field:
(17-11)
The sudden discharge of electric energy can be
harmful or fatal. Capacitors can retain their charge
indefinitely even when disconnected from a
voltage source – be careful!
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Capacitors and Capacitance (Key Equations)
Capacitance
• C = |Q| / |Delta V|
• Property of the conductors and the dielectric
Special Case - Parallel Plate Capacitor
• C = Kappa * Epsilon0*A / d
Energy
• Pee = 1/2 |Q| |Delta V|
• |Delta V| = Ed
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Slide 21-16
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
• Work-Energy Theorem
• 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
Electricity - concepts (Chs 20 & 21)
General Concepts - These are always true
Electric Force and Field Model
• Charge Model
• E-field
• Definition
Fe, s®t
E=
qt
Þ Fe, s®t = qE
• E-field vectors
• E-field lines
• Superposition
Exnet = E1x + E2 x + E3x + ×××
Energy, Electric Potential Energy, and Electric Potential
• Energy Definitions: KE, PEe, Peg, W, Esys, Eth and V
• Work-Energy Theorem
• Conservation of Energy
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Electricity - General key concepts (Chs 20 & 21)
Charge Model
• Electric forces can be attractive or repulsive
• Objects with the same sign of charge repel each other
• Objects with the opposite sign of charge attract each other
• Neutral objects are polarized by charged objects which creates
attractive forces between them
• There are two kinds of charges, positive (protons) and negative (electrons).
In solids, electrons are charge carriers (protons are 2000 time more
massive).
• A charged object has a deficit of electrons (+) or a surplus of electrons (-).
Neutral objects have equal numbers of + and – charges
• Fe gets weaker with distance: Fe α 1/r2
• Fe between charged tapes are > Fe between charged tapes & neutral objects
• Rubbing causes some objects to be charged by charge separation
• Charge can be transferred by contact, conduction, and induction
• Visualization => charge diagrams
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Slide 21-16
Nature of Electric Field Vectors
• Test charge is a small positive charge to sample the E-Field
• Charge of test charge is small compared to source charges
(source charges are the charges that generate the field)
• E-field vectors
• E-field is the force per charge E = Fe / q
• E-field vectors points away from + charges
• E-field vectors point towards - charges
• E-field for point charges gets weaker as distance from
source point charges increases
• For a point charge E = Fe / q = [k Q q / r2] / q = k Q / r2
• Electric Force Fe = qE
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Nature of Electric Field Lines
• E-Field lines start on + charges and end on -- charges
• Larger charges will have more field lines going out/coming in
• Density of Field lines is a measure of field strength – the higher
the density the stronger the field
• The E-field vector at a point in space is tangent to the field line
at that point. If there is no field line, extrapolate
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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
different types
PE f + DEth
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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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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Assembling a square of charges
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Slide 21-16
Analyzing a square of charges
Energy to Assemble
Wme = 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 = ΔPEE = PEEf - PEEi
= q2qV123@center - q2qV123@corner
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Problem 21.51
A -10.0 point charge and a +20.0 point charge are
15.0 apart on the x-axis.
Part A. What is the electric potential at the point on
the x-axis where the electric field is zero?
Do not consider x = + or - infinity.
Part B. What is the magnitude of the electric field at
the point between the charges on the x-axis where
the electric potential is zero?
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Slide 21-16
Problem 21.65
Two 2.2 -diameter disks spaced 1.9 apart form a parallel-plate
capacitor. The electric field between the disks is 4.6×105 V/m.
Part A. What is the voltage across the capacitor?
Part B. How much charge is on each disk
Part C. An electron is launched from the negative plate.
It strikes the positive plate at a speed of 2.1×107 m/s.
What was the electron's speed as it left the negative
plate?
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Slide 21-16
Problem 21.69
A proton is fired from far away toward the nucleus of an
iron atom. Iron is element number 26, and the diameter
of the nucleus is 9.0 fm. (1 fm = 1e-15 m.)
Assume the nucleus remains at rest.
What initial speed does the proton need to just reach
the surface of the nucleus?
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Slide 21-16
Example Problem
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).
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Slide 21-26
Example Problem
What is Q2?
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Slide 21-35
A Conductor in Electrostatic Equilibrium
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Slide 21-27
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
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
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Slide 21-25
Electric Potential of a Point Charge
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
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.
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
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