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Chapter 30. Potential and Field
To understand the
production of electricity by
solar cells or batteries, we
must first address the
connection between electric
potential and electric field.
Chapter Goal: To
understand how the electric
potential is connected to the
electric field.
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Chapter 30. Potential and Field
Topics:
• Connecting Potential and Field
• Sources of Electric Potential
• Finding the Electric Field from the
Potential
• A Conductor in Electrostatic Equilibrium
• Capacitance and Capacitors
• The Energy Stored in a Capacitor
• Dielectrics
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Chapter 30. Reading Quizzes
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What quantity is represented by
the symbol ?
A. Electronic potential
B. Excitation potential
C. EMF
D. Electric stopping power
E. Exosphericity
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What quantity is represented by
the symbol ?
A. Electronic potential
B. Excitation potential
C. EMF
D. Electric stopping power
E. Exosphericity
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What is the SI unit of capacitance?
A. Capaciton
B. Faraday
C. Hertz
D. Henry
E. Exciton
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What is the SI unit of capacitance?
A. Capaciton
B. Faraday
C. Hertz
D. Henry
E. Exciton
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The electric field
A. is always perpendicular to an
equipotential surface.
B. is always tangent to an
equipotential surface.
C. always bisects an equipotential
surface.
D. makes an angle to an equipotential
surface that depends on the amount
of charge.
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The electric field
A. is always perpendicular to an
equipotential surface.
B. is always tangent to an
equipotential surface.
C. always bisects an equipotential
surface.
D. makes an angle to an equipotential
surface that depends on the amount
of charge.
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This chapter investigated
A.
B.
C.
D.
E.
parallel capacitors
perpendicular capacitors
series capacitors.
Both a and b.
Both a and c.
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This chapter investigated
A.
B.
C.
D.
E.
parallel capacitors
perpendicular capacitors
series capacitors.
Both a and b.
Both a and c.
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Chapter 30. Basic Content and Examples
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Finding the Potential from the Electric Field
The potential difference between two points in space is
where s is the position along a line from point i to point f.
That is, we can find the potential difference between two
points if we know the electric field.
We can think of an integral as an area under a curve. Thus a
graphical interpretation of the equation above is
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Tactics: Finding the potential from the electric
field
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EXAMPLE 30.2 The potential of a parallelplate capacitor
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EXAMPLE 30.2 The potential of a parallelplate capacitor
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EXAMPLE 30.2 The potential of a parallelplate capacitor
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EXAMPLE 30.2 The potential of a parallelplate capacitor
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EXAMPLE 30.2 The potential of a parallelplate capacitor
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Batteries and emf
The potential difference between the terminals of an ideal
battery is
In other words, a battery constructed to have an emf of
1.5V creates a 1.5 V potential difference between its
positive and negative terminals.
The total potential difference of batteries in series is simply
the sum of their individual terminal voltages:
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Finding the Electric Field from the Potential
In terms of the potential, the component of the electric field
in the s-direction is
Now we have reversed Equation 30.3 and have a way to
find the electric field from the potential.
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EXAMPLE 30.4 Finding E from the slope of V
QUESTION:
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EXAMPLE 30.4 Finding E from the slope of V
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EXAMPLE 30.4 Finding E from the slope of V
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EXAMPLE 30.4 Finding E from the slope of V
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EXAMPLE 30.4 Finding E from the slope of V
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EXAMPLE 30.4 Finding E from the slope of V
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Kirchhoff’s Loop Law
For any path that starts and ends at the same point
Stated in words, the sum of all the potential differences
encountered while moving around a loop or closed path
is zero.
This statement is known as Kirchhoff’s loop law.
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Capacitance and Capacitors
The ratio of the charge Q to the potential difference ΔVC is
called the capacitance C:
Capacitance is a purely geometric property of two
electrodes because it depends only on their surface area and
spacing. The SI unit of capacitance is the farad:
1 farad = 1 F = 1 C/V.
The charge on the capacitor plates is directly
proportional to the potential difference between the
plates.
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EXAMPLE 30.6 Charging a capacitor
QUESTIONS:
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EXAMPLE 30.6 Charging a capacitor
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EXAMPLE 30.6 Charging a capacitor
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EXAMPLE 30.6 Charging a capacitor
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Combinations of Capacitors
If capacitors C1, C2, C3, … are in parallel, their equivalent
capacitance is
If capacitors C1, C2, C3, … are in series, their equivalent
capacitance is
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The Energy Stored in a Capacitor
• Capacitors are important elements in electric circuits
because of their ability to store energy.
• The charge on the two plates is ±q and this charge
separation establishes a potential difference ΔV = q/C
between the two electrodes.
• In terms of the capacitor’s potential difference, the
potential energy stored in a capacitor is
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EXAMPLE 30.9 Storing energy in a capacitor
QUESTIONS:
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EXAMPLE 30.9 Storing energy in a capacitor
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EXAMPLE 30.9 Storing energy in a capacitor
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The Energy in the Electric Field
The energy density of an electric field, such as the one
inside a capacitor, is
The energy density has units J/m3.
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Dielectrics
• The dielectric constant, like density or specific heat, is a
property of a material.
• Easily polarized materials have larger dielectric constants
than materials not easily polarized.
• Vacuum has κ = 1 exactly.
• Filling a capacitor with a dielectric increases the
capacitance by a factor equal to the dielectric constant.
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Chapter 30. Summary Slides
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General Principles
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General Principles
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General Principles
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Important Concepts
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Important Concepts
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Applications
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Applications
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Chapter 30. Clicker Questions
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What total potential difference is
created by these three batteries?
A. 1.0 V
B. 2.0 V
C. 5.0 V
D. 6.0 V
E. 7.0 V
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What total potential difference is
created by these three batteries?
A. 1.0 V
B. 2.0 V
C. 5.0 V
D. 6.0 V
E. 7.0 V
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Which potential-energy
graph describes this
electric field?
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Which potential-energy
graph describes this
electric field?
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Which set of equipotential surfaces
matches this electric field?
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Which set of equipotential surfaces
matches this electric field?
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Three charged, metal
spheres of different radii
are connected by a thin
metal wire. The potential
and electric field at the
surface of each sphere
are V and E. Which of
the following is true?
A.
B.
C.
D.
E.
V1 = V2 = V3 and E1 > E2 > E3
V1 > V2 > V3 and E1 = E2 = E3
V1 = V2 = V3 and E1 = E2 = E3
V1 > V2 > V3 and E1 > E2 > E3
V3 > V2 > V1 and E1 = E2 = E3
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Three charged, metal
spheres of different radii
are connected by a thin
metal wire. The potential
and electric field at the
surface of each sphere
are V and E. Which of
the following is true?
A.
B.
C.
D.
E.
V1 = V2 = V3 and E1 > E2 > E3
V1 > V2 > V3 and E1 = E2 = E3
V1 = V2 = V3 and E1 = E2 = E3
V1 > V2 > V3 and E1 > E2 > E3
V3 > V2 > V1 and E1 = E2 = E3
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Rank in order, from largest to smallest, the
equivalent capacitance (Ceq)a to (Ceq)d of
circuits a to d.
A. (Ceq)d > (Ceq)b > (Ceq)a > (Ceq)c
B. (Ceq)d > (Ceq)b = (Ceq)c > (Ceq)a
C. (Ceq)a > (Ceq)b = (Ceq)c > (Ceq)d
D. (Ceq)b > (Ceq)a = (Ceq)d > (Ceq)c
E. (Ceq)c > (Ceq)a = (Ceq)d > (Ceq)b
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Rank in order, from largest to smallest, the
equivalent capacitance (Ceq)a to (Ceq)d of
circuits a to d.
A. (Ceq)d > (Ceq)b > (Ceq)a > (Ceq)c
B. (Ceq)d > (Ceq)b = (Ceq)c > (Ceq)a
C. (Ceq)a > (Ceq)b = (Ceq)c > (Ceq)d
D. (Ceq)b > (Ceq)a = (Ceq)d > (Ceq)c
E. (Ceq)c > (Ceq)a = (Ceq)d > (Ceq)b
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