Transcript Powerpoint

Chapter 21
Electric Potential
Topics:
• Electric potential energy
• Electric potential
• Conservation of energy
• Capacitors and
Capacitance
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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The Capacitance of a Parallel-Plate Capacitor
e0 A
C=
d
Slide 21-31
Energy stored in Capacitor – Storing Energy in E-field
A charged capacitor stores electric energy; the energy stored is
equal to the work done to charge the capacitor.
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Slide 21-16
Capacitors
Note: Battery is a source of constant potential
What happens when you pull the plates of a capacitor
apart?
• With a Battery connected
• With no Battery connected
Do the following quantities (a) increase, (b) decrease, or
(c) remain the same:
• Charge
• E-Field
• Delta V
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Slide 21-16
Dielectrics and Capacitors
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.
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 A
C=
d
Dielectric strength is the maximum
field a dielectric can experience
without breaking down.
E' =
E0
k
Energy stored in Capacitor – Storing Energy in E-field
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Slide 21-16
Energy Model
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Slide 21-16
Capacitance Model
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Slide 21-16
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!
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
Properties of a Current
Slide 22-8
Light the Bulb
Can you light a bulb when you have
• 1 battery
• 1 Bulb
• 1 wire
• A - yes
• B - no
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Slide 21-16
Definition of a Current
Slide 22-9
Storage of Electric Energy
Heart defibrillators use electric
discharge to “jump-start” the heart,
and can save lives.
The Electrocardiogram (ECG or EKG)
The electrocardiogram
detects heart defects by
measuring changes in
potential on the surface of
the heart.
Capacitors
Note: Battery is a source of constant potential
What happens when you insert a dielectric?
• With a Battery connected
• With no Battery connected
Do the following quantities (a) increase, (b) decrease, or
(c) remain the same:
•
Charge
•
E-Field
•
Delta V
•
Energy stored
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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
• E-field lines
r
Fe, st
E
qt
r
r
 Fe, st  qE
Exnet   Ex  E1x  E2 x  E3x  
• Superposition
(note that for forces and fields,
we need to work in vector components)
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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

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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
r
Fe, st
E
qt
r
r
 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
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
Chapter 21 Key Equations (Physics 151)
Key Energy Equations from Physics 151
Definition of Work
r
r r
r
Work W  F g r  F r cos 
Where   angle between the vectors
Work- Energy Theorem (only valid when particle model applies)
Wnet  KE
Work done by a conservative force (Fg, Fs, & Fe)
Wg  PEg Also work done by conservative force
is path independent
Conservation of Energy Equation
KEi 

PEi   Esys  KE f 
different types
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
different types
PE f  Eth
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
r
r
PEe  We    Fe  r cos      q E r cos 
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
PEe
We
V 

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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