Transcript Lecture 10 review

Lecture 10
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Chapter
Chapter
Chapter
Chapter
15
16
17
18
Fig. 15-CO, p.497
First Observations –
Greeks
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Observed electric and magnetic
phenomena as early as 700 BC
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Found that amber, when rubbed,
became electrified and attracted
pieces of straw or feathers
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Also discovered magnetic forces by
observing magnetite attracting iron
Fig. 15-1b, p.498
Fig. 15-2, p.499
Fig. 15-3a, p.499
Fig. 15-1, p.498
Properties of Charge, final
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Charge is quantized
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All charge is a multiple of a fundamental
unit of charge, symbolized by e
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Quarks are the exception
Electrons have a charge of –e
Protons have a charge of +e
The SI unit of charge is the Coulomb (C)
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e = 1.6 x 10-19 C
Conductors
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Conductors are materials in which
the electric charges move freely in
response to an electric force
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Copper, aluminum and silver are good
conductors
When a conductor is charged in a
small region, the charge readily
distributes itself over the entire
surface of the material
Insulators
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Insulators are materials in which
electric charges do not move freely
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Glass and rubber are examples of
insulators
When insulators are charged by
rubbing, only the rubbed area
becomes charged
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There is no tendency for the charge to
move into other regions of the material
Semiconductors
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The characteristics of
semiconductors are between those
of insulators and conductors
Silicon and germanium are
examples of semiconductors
Charging by Conduction
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A charged object (the
rod) is placed in contact
with another object (the
sphere)
Some electrons on the
rod can move to the
sphere
When the rod is
removed, the sphere is
left with a charge
The object being charged
is always left with a
charge having the same
sign as the object doing
the charging
Fig. 15-5a, p.501
Fig. 15-5b, p.501
Coulomb’s Law
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Coulomb shows that an electrical force
has the following properties:
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It is along the line joining the two particles
and inversely proportional to the square of
the separation distance, r, between them
It is proportional to the product of the
magnitudes of the charges, |q1|and |q2|on
the two particles
It is attractive if the charges are of opposite
signs and repulsive if the charges have the
same signs
Coulomb’s Law, cont.
q1 q2
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Mathematically, F  k e
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ke is called the Coulomb Constant
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ke = 8.9875 x 109 N m2/C2
Typical charges can be in the µC range
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r2
Remember, Coulombs must be used in the
equation
Remember that force is a vector
quantity
Applies only to point charges
Coulomb's law
Characteristics of Particles
Fig. 15-6a, p.502
Fig. 15-6b, p.502
Electrical Forces are Field
Forces
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This is the second example of a field
force
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Gravity was the first
Remember, with a field force, the force
is exerted by one object on another
object even though there is no physical
contact between them
There are some important similarities
and differences between electrical and
gravitational forces
The Superposition
Principle
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The resultant force on any one
charge equals the vector sum of
the forces exerted by the other
individual charges that are
present.
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Remember to add the forces as
vectors
Fig. 15-8, p.504
Electrical Forces are Field
Forces
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This is the second example of a field
force
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Gravity was the first
Remember, with a field force, the force
is exerted by one object on another
object even though there is no physical
contact between them
There are some important similarities
and differences between electrical and
gravitational forces
Electrical Force Compared
to Gravitational Force
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Both are inverse square laws
The mathematical form of both laws is
the same
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Masses replaced by charges
Electrical forces can be either attractive
or repulsive
Gravitational forces are always
attractive
Electrostatic force is stronger than the
gravitational force
The Superposition
Principle
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The resultant force on any one
charge equals the vector sum of
the forces exerted by the other
individual charges that are
present.
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Remember to add the forces as
vectors
Fig. 15-8, p.504
Superposition Principle
Example
The force exerted
by q1 on q3 is F13
 The force exerted
by q2 on q3 is F23
 The total force
exerted on q3 is
the vector sum of
F13and F23
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Fig. 15-9, p.505
Electric Field
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ke Q
F
Mathematically, E 
 2
qo
r
SI units are N / C
Use this for the magnitude of the field
The electric field is a vector quantity
The direction of the field is defined to
be the direction of the electric force that
would be exerted on a small positive
test charge placed at that point
Direction of Electric Field
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The electric field
produced by a
negative charge is
directed toward
the charge
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A positive test
charge would be
attracted to the
negative source
charge
Electric Field Lines
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A convenient aid for visualizing
electric field patterns is to draw
lines pointing in the direction of
the field vector at any point
These are called electric field
lines and were introduced by
Michael Faraday
Fig. 15-13a, p.510
Fig. 15-13b, p.510
Electric Field Line Patterns
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An electric dipole
consists of two
equal and
opposite charges
The high density
of lines between
the charges
indicates the
strong electric
field in this region
Electric Field Line Patterns
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Two equal but like point
charges
At a great distance from
the charges, the field
would be approximately
that of a single charge of
2q
The bulging out of the
field lines between the
charges indicates the
repulsion between the
charges
The low field lines
between the charges
indicates a weak field in
this region
Electric Field Patterns
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Unequal and
unlike charges
Note that two
lines leave the
+2q charge for
each line that
terminates on -q
Fig. 15-18a, p.513
Fig. 15-18b, p.513
Van de Graaff
Generator
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An electrostatic generator
designed and built by
Robert J. Van de Graaff in
1929
Charge is transferred to
the dome by means of a
rotating belt
Eventually an
electrostatic discharge
takes place
Electrical Potential Energy
of Two Charges
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V1 is the electric
potential due to q1 at
some point P
The work required to
bring q2 from infinity to
P without acceleration
is q2V1
This work is equal to
the potential energy of
the two particle system
q1q2
PE  q2 V1  k e
r
The Electron Volt
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The electron volt (eV) is defined as the
energy that an electron gains when
accelerated through a potential
difference of 1 V
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Electrons in normal atoms have energies of
10’s of eV
Excited electrons have energies of 1000’s of
eV
High energy gamma rays have energies of
millions of eV
1 eV = 1.6 x 10-19 J
Equipotential Surfaces
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An equipotential surface is a
surface on which all points are at
the same potential
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No work is required to move a charge
at a constant speed on an
equipotential surface
The electric field at every point on an
equipotential surface is perpendicular
to the surface
Equipotentials and Electric
Fields Lines – Positive Charge
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The equipotentials
for a point charge
are a family of
spheres centered on
the point charge
The field lines are
perpendicular to the
electric potential at
all points
Equipotentials and Electric
Fields Lines – Dipole
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Equipotential lines
are shown in blue
Electric field lines
are shown in red
The field lines are
perpendicular to
the equipotential
lines at all points
Capacitance, cont
Q
 C 
V
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Units: Farad (F)
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1F=1C/V
A Farad is very large
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Often will see µF or pF
Parallel-Plate Capacitor
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The capacitance of a device
depends on the geometric
arrangement of the conductors
For a parallel-plate capacitor
whose plates are separated by air:
A
C  o
d
Parallel-Plate Capacitor,
Example
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The capacitor consists of
two parallel plates
Each have area A
They are separated by a
distance d
The plates carry equal and
opposite charges
When connected to the
battery, charge is pulled off
one plate and transferred to
the other plate
The transfer stops when
Vcap = Vbattery
Demo 2
Capacitors in Parallel
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The total charge is
equal to the sum of
the charges on the
capacitors
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Qtotal = Q1 + Q2
The potential
difference across the
capacitors is the
same
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And each is equal to
the voltage of the
battery
Fig. 16-19, p.551
Fig. 16-20, p.552
Fig. P16-34, p.564
Fig. 16-21, p.553
Energy Stored in a
Capacitor
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Energy stored = ½ Q ΔV
From the definition of capacitance,
this can be rewritten in different
forms
2
1
1
Q
Energy  QV  CV 2 
2
2
2C
Dielectric Strength
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For any given plate separation,
there is a maximum electric field
that can be produced in the
dielectric before it breaks down
and begins to conduct
This maximum electric field is
called the dielectric strength
Table 16-1, p.557
Electric Current
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Whenever electric charges of like signs
move, an electric current is said to exist
The current is the rate at which the
charge flows through this surface
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Look at the charges flowing perpendicularly
to a surface of area A
Q
I 
t
The SI unit of current is Ampere (A)
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1 A = 1 C/s
Electric Current, cont
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The direction of the current is the
direction positive charge would flow
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This is known as conventional current
direction
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In a common conductor, such as copper, the
current is due to the motion of the negatively
charged electrons
It is common to refer to a moving
charge as a mobile charge carrier
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A charge carrier can be positive or negative
Current and Drift Speed
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Charged particles
move through a
conductor of crosssectional area A
n is the number of
charge carriers per
unit volume
n A Δx is the total
number of charge
carriers
Current and Drift Speed,
cont
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The total charge is the number of
carriers times the charge per carrier, q
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The drift speed, vd, is the speed at
which the carriers move
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ΔQ = (n A Δx) q
vd = Δx/ Δt
Rewritten: ΔQ = (n A vd Δt) q
Finally, current, I = ΔQ/Δt = nqvdA
Current and Drift Speed,
final
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If the conductor is isolated, the
electrons undergo random motion
When an electric field is set up in
the conductor, it creates an electric
force on the electrons and hence a
current
Charge Carrier Motion in a
Conductor
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The zig-zag black
line represents the
motion of charge
carrier in a
conductor
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The net drift speed is
small
The sharp changes in
direction are due to
collisions
The net motion of
electrons is opposite
the direction of the
electric field Demo
p.578
Resistance
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In a conductor, the voltage applied
across the ends of the conductor is
proportional to the current through
the conductor
The constant of proportionality is
the resistance of the conductor
V
R
I
Fig. 17-CO, p.568
Resistance, cont
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Units of resistance are ohms (Ω)
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1Ω=1V/A
Resistance in a circuit arises due to
collisions between the electrons
carrying the current with the fixed
atoms inside the conductor
Ohm’s Law
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Experiments show that for many
materials, including most metals, the
resistance remains constant over a wide
range of applied voltages or currents
This statement has become known as
Ohm’s Law
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ΔV = I R
Ohm’s Law is an empirical relationship
that is valid only for certain materials
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Materials that obey Ohm’s Law are said to
be ohmic
Resistivity
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The resistance of an ohmic conductor is
proportional to its length, L, and
inversely proportional to its crosssectional area, A
L
R
A
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ρ is the constant of proportionality and is
called the resistivity of the material
Table 17-1, p.576
Temperature Variation of
Resistivity
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For most metals, resistivity
increases with increasing
temperature
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With a higher temperature, the
metal’s constituent atoms vibrate
with increasing amplitude
The electrons find it more difficult to
pass through the atoms
Temperature Variation of
Resistivity, cont
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For most metals, resistivity increases
approximately linearly with temperature
over a limited temperature range
  o [1  (T  To )]
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ρ is the resistivity at some temperature T
ρo is the resistivity at some reference
temperature To
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To is usually taken to be 20° C = 68 ° F
 is the temperature coefficient of resistivity
Temperature Variation of
Resistance
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Since the resistance of a conductor
with uniform cross sectional area is
proportional to the resistivity, you
can find the effect of temperature
on resistance
R  Ro [1 (T  To )]
Electrical Energy and
Power, cont
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The rate at which the energy is
lost is the power
Q

V  I V
t
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From Ohm’s Law, alternate forms
of power are
V
 I R 
R
2
2
Electrical Energy and
Power, final
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The SI unit of power is Watt (W)
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I must be in Amperes, R in ohms and
V in Volts
The unit of energy used by electric
companies is the kilowatt-hour
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This is defined in terms of the unit of
power and the amount of time it is
supplied
1 kWh = 3.60 x 106 J
Fig. Q18-13, p.616
More About the Junction
Rule
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I1 = I 2 + I3
From
Conservation of
Charge
Diagram b shows
a mechanical
analog
RC Circuits
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A direct current circuit may contain
capacitors and resistors, the current will
vary with time
When the circuit is completed, the
capacitor starts to charge
The capacitor continues to charge until
it reaches its maximum charge (Q = Cε)
Once the capacitor is fully charged, the
current in the circuit is zero
Charging Capacitor in an
RC Circuit
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The charge on the
capacitor varies with
time
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q = Q(1 – e-t/RC)
The time constant,
=RC
The time constant
represents the time
required for the
charge to increase
from zero to 63.2%
of its maximum
Notes on Time Constant
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In a circuit with a large time
constant, the capacitor charges
very slowly
The capacitor charges very quickly
if there is a small time constant
After t = 10 , the capacitor is over
99.99% charged
Household Circuits
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The utility company
distributes electric
power to individual
houses with a pair of
wires
Electrical devices in
the house are
connected in parallel
with those wires
The potential
difference between
the wires is about
120V
Effects of Various Currents
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5 mA or less
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10 mA
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Can cause a sensation of shock
Generally little or no damage
Hand muscles contract
May be unable to let go a of live wire
100 mA
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If passes through the body for just a few
seconds, can be fatal