Transcript Powerpoint

Chapter 21
Electric Potential
Topics:
• Electric potential energy
• Electric potential
• Conservation of energy
• Equipotential
• Contour Maps
• 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?
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Slide 21-1
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
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
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
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
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
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)
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
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)
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
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
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
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 V
• Higher potential as you approach a positive charge; lower potential as you
approach a negative charge
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Slide 21-16
Connecting Potential and Field
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
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.
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
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.
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
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?
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Slide 21-33
Graphical Representations of Electric Potential
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
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
Discussion of other units for Energy and E-field
eV – electron Volts => Unit of energy for particle accelerators
The energy gained by an electron that goes through a potential
difference of one volt
1 eV = 1.60 x 10-19 J
V/m – Volts per meter => Unit of Electric Field
|Delta V| = |E||Delta r| => |E| = |Delta V| / |Delta r|
[E] = V / m
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Slide 21-16
Batteries
The potential difference
between the terminals of a
battery, often called the
terminal voltage, is the
battery’s emf.
W
chem
∆Vbat = ____
=e
q
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Slide 22-12
Parallel Plate Capacitor
A capacitor consists of two conductors that are
close but not touching. A capacitor has the
ability to store electric charge.
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Slide 21-16
Parallel Plate Capacitor
(a) Parallel-plate capacitor connected to battery.
(b) Battery and Capacitor in a circuit diagram.
Relationship of E-field & Delta V?
Delta V
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Slide 21-16
Define Capacitance
Capacitance is a measure of how much charge can be stored in a
capacitor for a given amount of voltage
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Slide 21-16
The Capacitance of a Parallel-Plate Capacitor
e0 A
C=
d
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Slide 21-31
Capacitance and Capacitors
The charge ±Q on each
electrode is proportional to the
potential difference ΔVC between
the electrodes:
Q = C DVC
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Slide 21-29
Charging a Capacitor
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Slide 21-30
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
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Slide 21-16
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.
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Slide 21-16
Dielectrics and Capacitors
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
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.
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
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
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
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!
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
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
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Slide 21-16