Transcript Powerpoint

Chapter 21
Electric Potential
Topics:
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Conservation of energy
Work and Delta PE
Electric potential energy
Electric potential
Contour Maps
E-Field and Equipotential
Conductors & Fields
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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Slide 21-1
Chapter 21 Key Energy Equations
Key Energy Equations from Physics 151 and Ch. 21 so far
Definition of Work
Work W = F i Dr = F Dr cos a
Where a = angle between the vectors
Work done by a conservative force (Fg, Fs, & Fe) We = -DUe
Also work done by conservative force is path independent => Wext = - We
Conservation of Energy Equation
(can ignore Ug and Us unless they are relevant)
Ki +
å
Ui + D Esys = K f +
different types
å
U f + DEth
different types
Electric Energy – Special Cases (Similar equations for gravity)
2 Point Charges
Charge in a
Uniform E-field
q1q2
Ue = k
r12
DUe = -We = - éë Fe × Dr cos a ùû = - q E Dr cos a
Note: in both cases of Electric Energy must assume where Ue = 0
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Slide 21-16
Chapter 21 Key Equations (3)
Key Points about Electric Potential
Electric Potential is the Electric Energy per Charge
Ue
V=
qtest
DUe
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 Delta V= 0 V is an equipotential line
(The electric force does zero work on a test charge that moves
on an equipotential line and Delta PEe= 0 J)
For multiple source charges
VPOI = V1@POI + V2@POI + …
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Slide 21-16
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
DPEe
We
Fe i Dr
qtest E i Dr
DV =
==== -E i Dr = - E Dr cos a
qtest
qtest
qtest
qtest
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Slide 21-25
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Electric field of a charged conductor
Free electrons in a conductor are quickly redistributed
until equilibrium is reached, at which point the E field
inside the conductor and parallel to its surface
becomes zero.
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Electric field outside a charged conductor
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Grounding
• Grounding discharges
an object made of
conducting material by
connecting it to Earth.
• Electrons will move
between and within
the spheres until the V
field on the surfaces of
and within both
spheres achieves the
same value.
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Example Problem
What is Q2?
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Slide 21-35
Uncharged conductor in an electric field:
• The free electronsShielding
inside the object become
redistributed due to electric forces, until the E field
within the conducting object is reduced to zero.
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Uncharged conductor in an electric field:
Shielding
The interior is protected from the external field—an effect called
shielding.
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Dielectric materials in an electric field
• If an atom in a dielectric
material resides in a region
with an external electric field,
the nucleus and the electrons
are displaced slightly in
opposite directions until the
force that the field exerts on
each of them is balanced by
the force they exert on each
other.
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Polar water molecules in
an external electric field
• Some molecules, such as water, are
natural electric dipoles even when the
external E field is zero.
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E field inside a dielectric
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A dielectric material cannot
completely shield its interior
from an external electric field,
but it does decrease the field.
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E field inside a dielectric
• Physicists use a physical quantity to
characterize the ability of dielectrics to decrease
the E field:
• The dielectric constant κ
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Dielectric constants for
different types of
materials
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Electric force and dielectrics
The force that object 1 exerts on object 2 is reduced by κ
compared with the force it would exert in a vacuum.
Inside the dielectric material, Coulomb's law is now written
as:
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Salt dissolves in blood but not in air
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When salt is placed in water or blood:
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Many more collisions occur between
molecules than between molecules and air;
these can break an ion free from the crystal.
Any ions that become separated do not exert
nearly as strong as an attractive force on
each other because of the dielectric effect.
The random kinetic energy of the liquid is
sufficient to keep the sodium and chlorine
ions from recombining, allowing the nervous
system to use the freed sodium ions to
transmit information.
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Tip
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Capacitors
A capacitor consists of two conducting surfaces separated by a
nonconducting material. Charges on the two conductors must
have charges with equal magnitude and opposite sign.
The role of a capacitor is to store electric energy
(AKA Electric Potential Energy Ue).
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Capacitors (Cont'd)
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Capacitors
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If we consider the capacitor plates to be large
flat conductors, charge should be distributed
evenly on the plates.
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The magnitude of the E field between the
plates relates to the potential difference from
one plate to the other and the distance
separating them
To double the E field, the charge on other
plates has to double.
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Capacitors
• The proportionality constant C in this equation is
called the capacitance of the capacitor.
• The unit of capacitance is 1 coulomb/volt = 1
farad (in honor of Michael Faraday).
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Capacitance of a capacitor
• A capacitor with larger-surface-area
plates should be able to maintain more
charge separation because there is more
room for the charge to spread out.
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Capacitance of a capacitor
A larger distance between the plates leads to a
smaller-magnitude E field between the plates.
Because the magnitude of this E field is
proportional to the amount of electric charge on
the plates, a larger plate separation leads to a
smaller-magnitude electric charge on the plates.
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Capacitance of a capacitor
Material between the plates with a large
dielectric constant becomes polarized by the
electric field between the plates. Thus more
charge moves onto capacitor plates that are
separated by material of high dielectric
constant.
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Capacitance of a capacitor
• The capacitance of a particular capacitor
should increase if the surface area A of
the plates increases, decrease if the
distance d between them is increased,
and increase if the dielectric constant k of
the material between them increases:
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Tip
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Energy of a charged capacitor
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To determine the electric potential
energy in a charged capacitor, we
start with an uncharged capacitor
and then calculate the amount of
work that must be done on the
capacitor to move electrons from
one plate to the other.
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Energy of a charged capacitor
• The process of charging a capacitor is
similar to stretching a spring: at the
beginning, a smaller force is needed to
stretch the spring by a certain amount
compared to the much greater force
needed when the spring is already
stretched.
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Lightning
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When the E field in air or in some other material
is very large, free electrons accelerate and
quickly acquire enough kinetic energy to ionize
atoms and molecules in their path when colliding
with them.
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Lightning rods
• Dielectric breakdown
occurs between the
cloud and the lightning
rod.
• Drawing lightning to the
rod and away from the
building prevents
damage to the building
and its inhabitants.
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Chapter 24
Magnetic Fields and Forces
Topics:
• Magnets and the magnetic
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field
Electric currents create
magnetic fields
Magnetic fields of wires,
loops, and solenoids
Magnetic forces on charges
and currents
Magnets and magnetic
materials
Sample question:
This image of a patient’s knee was made with magnetic fields, not
x rays. How can we use magnetic fields to visualize the inside of
the body?
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Slide 24-1
Key Points
• Three types of magnetic interactions
1. no interaction with either pole of a magnet
=> object is non-magnetic
2. attracted to both poles of a magnet
=> object is magnetic
3. Attracted to one pole and repelled by the other pole
=> object is a magnet
• Magnetic field vector from a bar magnet is a super position of
the magnetic field vectors from the N and S poles:
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Vector from N pole points away from N pole
Vector from S pole points towards S pole
• Field lines form complete loops inside and outside of magnet
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Field lines outside magnet go from N to S poles
Field lines inside magnet go from S to N poles
Magnetic Field vectors at a point are tangential to Magnetic Field Lines
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3-D Arrows, Cross Products, and Right Hand Rule 1
• Showing vectors in 3D (need this for magnetic
force)
C = A´ B
• Cross
C = AProduct
B sin a
For direction use Right-hand rule 1
• Right-hand rule 1 (RHR 1)
=> forCfinding
= A ´ Bdirection of cross-product vector
(Cross-Product Rule)
1. Point right hand in the direction of the first vector (vector A)
2. Rotate your right hand until you can point your fingers in the
direction of the second vector (vector B)
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Slide 24-2
Right Hand Rules for Magnetism
• Right-hand rule 1 (RHR 1) => for finding magnetic force
FB= q*v_vector x B_vector (Cross-Product Rule)
1. Point right hand in the direction the charges are moving (current or velocity)
2. Rotate your right hand until you can point your fingers in the direction of the
magnetic Field
3. Thumb points in direction of force for + charge
Force is in opposite direction for - charges
• Right-hand rule 2 (RHR 2) => Finding direction of B from I
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Point thumb of right hand in direction of current I,
B-field lines curl in direction of fingers
• Right-hand rule 3 (RHR 3) =>
Finding direction of current in a loop from direction of B-field
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Point thumb of right hand in direction of B-field
Fingers of right hand curl in direction of current
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Slide 24-2
Electric Currents Also Create Magnetic Fields
A long, straight
wire
A current loop
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A solenoid
Slide 24-15
Drawing Field Vectors and Field Lines of a
Current-Carrying Wire
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Slide 24-21
The Magnitude of the Field due to a Long, Straight,
Current-Carrying Wire
m0 I
B=
2p r
m0 = permeability constant = 1.257 ´ 10 T× m/A
-6
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Slide 24-25
Drawing a Current Loop
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Slide 24-22
The Magnetic Field of a Current Loop
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Slide 24-23
The Magnetic Field of a Current Loop
B=
m0 I
2R
Magnetic field at the center of
a current loop of radius R
B=
m0 NI
2R
Magnetic field at the center of
a current loop with N turns
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Slide 24-29
The Magnetic Field of a Solenoid
A short solenoid
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A long solenoid
Slide 24-24
The Magnetic Field Inside a Solenoid
N
B = m0 I
L
Magnetic field inside a solenoid
of length L with N turns.
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Slide 24-31
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Body cells as capacitors
Cells, including nerve cells, have capacitor-like
properties.
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The conducting "plates" are the fluids on
either side of a moderately nonconducting
cell membrane.
In this membrane, chemical processes
cause ions to be "pumped" across the
membrane.
As a result, the membrane's inner surface
becomes slightly negatively charged, while
the outer surface becomes slightly positively
charged.
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Cell Capacitance Example
• Estimate:
1.The capacitance C of a single cell.
2.The charge separation q of all of the
membranes of the human body's 1013 cells.
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Assume that each cell has a surface area
of
A = 1.8 x 10−9 m2, a membrane thickness of
d = 8.0 x 10−9 m, ΔV = 0.070 across the
membrane wall, and a membrane dielectric
constant κ = 8.0.
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Quantitative Exercise
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Estimate the capacitance of your physics textbook,
assuming that the front and back covers (area A =
0.050 m2, separation d = 0.040 m) are made of a
conducting material. The dielectric constant of paper is
approximately 6.0.
Determine what the potential difference must be
across the covers for the textbook to have a charge
separation of
10−6 C (one plate has charge +10−6 C and the other
has charge −10−6 C).
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Energy of a charged capacitor
•
To determine the electric potential
energy in a charged capacitor, we
start with an uncharged capacitor
and then calculate the amount of
work that must be done on the
capacitor to move electrons from
one plate to the other.
Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Energy of a charged capacitor
• The process of charging a capacitor is
similar to stretching a spring: at the
beginning, a smaller force is needed to
stretch the spring by a certain amount
compared to the much greater force
needed when the spring is already
stretched.
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Quantitative Exercise
• In Example 15.10, we estimated that the
total charge separated across all the cell
membranes in a human body was about
11 C. Recall that the potential difference
across the cell membranes is 0.070 V.
Estimate the work that must be done to
separate the charges across the
membranes of the body's approximately
1013 cells.
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