SCS CS 139 39 App Appli lied ed Ph Physics ysics II II Dr. - - PowerPoint PPT Presentation
SCS CS 139 39 App Appli lied ed Ph Physics ysics II II Dr. Prapun Suksompong prapun@siit.tu.ac.th 1. Magnetic Forces and Fields www.prapun.com 2. Electromagnetic Induction 3. Alternating Current 4. Electromagnetic Wave Office Hours:
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prapun@siit.tu.ac.th www.prapun.com
Office Hours: Library (Rangsit) Mon 16:20-16:50 BKD 3601-7 Wed 9:20-11:20
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Ph.D. from Cornell University, USA In Electrical and Computer Engineering Minor: Mathematics (Probability Theory) Ph.D. Research: Neuro-Information Theory
Modeling and analyzing neurons in human brain
from communication engineering perspective.
Current Research: Wireless Communication
Mobile Communications, WiFi (802.11)
2009 SIIT Best Teaching Award 2011 SIIT Research Award
prapun.com
Please check the course website
regularly.
Announcements References Handouts (Posted before
corresponding lectures)
Annotated Notes/Slides (Posted
after corresponding lectures)
Assignments and Solutions
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Some PDF notes/slides will be posted before the corresponding
lectures.
Hard copies can be purchased from the copy center.
In lectures…
PDF notes/slides will be highlighted and updated with examples /
comments.
The annotated pdf files will be posted after the corresponding
lectures.
Put all of your energy into understanding the material.
Remind me the day after the lecture if the notes/slides from the
day before are still not posted on the web.
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B
F qv B F iL B
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6
Principles of Physics Ninth Edition, International Student Version David Halliday, Robert Resnick,
and Jearl Walker
Chapter 28 Magnetic Fields
28-1 What Is Physics? 28-2 What Produces a Magnetic Field? 28-3 The Definition of 𝐶 28-6 A Circulating Charged Particle 28-8 Magnetic Force on a Current-
Carrying Wire
28-9 Torque on a Current Loop
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Use moving electrically charged particles,
such as a current in a wire, to make an electromagnet.
Magnetic field is a basic characteristic of elementary particles
(such as electrons) just as mass and electric charge (or lack of charge) are basic characteristics.
These particles have an intrinsic magnetic field around them. Permanent magnet: The magnetic fields of the electrons in
certain materials add together to give a net magnetic field around the material.
In other materials, the magnetic fields of the electrons cancel
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You are surrounded by magnets. Old: Magnetic recording of music and images on audiotape and
videotape.
Magnets control CD and DVD players and computer hard drives. Magnets drive the speaker cones in headphones, TVs, computers,
and telephones.
A modern car comes equipped with dozens of magnets because
they are required in the motors for engine ignition, automatic window control, sunroof control, and windshield wiper control.
Most security alarm systems, doorbells, and automatic door
latches employ magnets.
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NeoCube, BuckyBalls, CyberCube, EuroCube, MagCube
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Credit, debit, and ATM cards: All of these cards have a
magnetic strip on one side.
The magstripe is made up of tiny iron-based magnetic
particles (about 20 millionths of an inch long) in a plastic-like film.
12
Hard disk drives record data on a thin magnetic coating
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Using an electromagnet to collect and transport scrap metal
at a steel mill.
15
the field around an ordinary bar magnet
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N N N N N NS N
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Magnetic field viewing film
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Turn off the iPad 2's screen. The rest are used to either clamp to the iPad on the right side (the far-right column of magnets), or to form the triangular shape used to create a stand for the iPad 2.
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Run from the north pole to the south pole.
bar magnet horseshoe magnet C-shaped magnet
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A vector quantity. We can represent magnetic fields
with field lines.
Rule 1: The direction of the tangent
to a magnetic field line at any point gives the direction of 𝐶 at that point
Rule 2: The spacing of the lines
represents the magnitude of 𝐶
The magnetic field is stronger where
the lines are closer together, and conversely.
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B = magnitude of 𝐶 SI Unit: tesla (T)
Defined in 1960 in honour of Nikola Tesla
Earlier non-SI unit: “gauss” 1 T (tesla) = 104 G (gauss) Some approximate magnetic fields:
Earth’s magnetic field near the planet’s surface:
1 G = 100 T
In magnetically shielded room
(MSR): 10-14 T = 10 fT
2
N N s T Cm/s Cm N N C/sm A m Wb m
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On Earth’s surface, we can detect magnetic field
with a compass, which is essentially a slender bar magnet.
The earth’s geographical
north pole is actually its magnetic south pole.
Magnetoception:
Migratory birds and sea turtles can sense the earth’s magnetic field, using it for navigation.
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Magnetoencephalography A powerful and noninvasive
method for studying human brain activity.
Work by detecting the tiny
(femtotesla) magnetic fluctuations at the surface of the head that arise from the brain’s electrical activity.
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Array of dots (which represent the
tips of arrows) represents a field directed out of the plane.
Array of Xs
represents a field directed into that plane.
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Charged particle moving through a magnetic field
experience magnetic force.
A magnetic field 𝐶
is defined in terms of the force 𝐺
𝐶
acting on a test particle with charge q moving through the field with velocity 𝑤 :
The magnitude of 𝐺
𝐶:
B
F qv B sin
B
F q vB
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A uniform magnetic field with magnitude 1.2 mT, is directed
vertically upward throughout the volume of a laboratory
from south to north with speed 3.2107 m/s.
What magnetic deflecting force acts on the proton as it
enters the chamber? (Neglect Earth’s magnetic field.)
𝐶
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Right-hand rule: The thumb of the right hand points in the
direction of 𝑤 × 𝐶 when the fingers sweep 𝑤 into 𝐶 .
Perpendicular to the direction of 𝑤 Perpendicular to the direction of 𝐶
B
F qv B
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A charged particle with mass m and charge magnitude |𝑟| moving with velocity 𝑤 perpendicular to a uniform magnetic field 𝐶 will travel in a circle. The magnetic force plays the role of centripetal force.
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33
The radius r of the circle is The period T is given by | | mv r q B 2 2 | | r m T v q B
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An ion of mass m (to be
measured) and charge q is produced in source S.
The initially stationary ion is
accelerated by the electric field due to a potential difference V.
The ion leaves S and enters a separator chamber in which a
uniform magnetic field is perpendicular to the path of the ion.
A wide detector lines the bottom wall of the chamber, and
the 𝐶 causes the ion to move in a semicircle and thus strike the detector.
35
Suppose that B = 80.000 mT, V = 1000.0 V
, and ions of charge q = +1.6022×10-19C strike the detector at a point that lies at x = 1.6254 m.
What is the mass m of the individual ions?
B
F
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A straight wire carrying a current i in a uniform magnetic field experiences a sideways force
F iL B sin F iLB
𝑀 is a length vector that has magnitude L and is directed along the wire segment in the direction of the (conventional) current.
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52
The permanent magnet creates a magnetic field that exerts forces
For a current I in the direction shown, the force is to the right. If the electric current in the voice coil oscillates, the speaker cone
attached to the voice coil oscillates at the same frequency.
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Note that it does not matter whether we
consider negative charges drifting downward in the wire (the actual case) or positive charges drifting upward. The direction of the deflecting force on the wire is the same.
dF idL B If the wire is not straight or the field is not uniform,
we can imagine the wire broken up into small straight segments.
In the differential limit, we can write
The force on the wire as a whole is then the vector sum of all the
forces on the segments that make it up.
40
Electric motor. A rectangular loop of wire,
carrying a current and free to rotate about a fixed axis, is placed in a magnetic field.
Magnetic forces on the wire
produce a torque that rotates the loop.
Side 2 Side 4
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To define the orientation of the
loop in the magnetic field, we use a normal vector 𝒐 that is perpendicular to the plane of the loop.
Useful Fact: The loop will rotate
so that 𝑜 has the same direction as 𝐶.
Right-hand rule: To find the direction
right hand in the direction of the current at any point on the loop. Your extended thumb then points in the direction of the normal vector .
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𝐺 1 = 𝐺 3 = 𝑗𝑏𝐶
The normal vector 𝑜 is shown at an arbitrary angle to the direction of 𝐶.
𝐺 2 = 𝐺
4 = 𝑗𝑐𝐶 sin 90 − 𝜄 = 𝑗𝑐𝐶 cos 𝜄
𝐺
2 and 𝐺
4 have the same magnitude but opposite directions.
Thus, they cancel out exactly. Their net force is zero.
𝐺
1 and 𝐺
3 have the same magnitude but opposite directions. Thus, they do not tend to move the loop up or down.
43
𝐺
2 and 𝐺
4: Their common line
net torque is also zero.
𝐺
1 and 𝐺 3: Do not share the same line of action; so they produce a net torque.
r F
2 sin sin sin 2 b iaB iabB iAB
Area enclosed by the coil
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Use a coil of N loops or turns Flat coil assumption: Assume that the turns are wound
tightly enough that they can be approximated as all having the same dimensions and lying in a plane.
Total torque The formula holds for all flat coils no matter what their
shape.
For the circular coil, we have sin NiAB
Area enclosed by the coil
2 sin
Ni r B
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magnet Think of the pencil as your finger
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2
ˆ 4
enc
i ds r dB r B ds i
2
Principles of Physics Ninth Edition, International Student Version David Halliday, Robert Resnick,
and JearlWalker
Chapter 29 Magnetic Fields due to
Currents
29-2 Calculating the Magnetic Field
Due to a Current
29-3 Force Between Two Parallel
Currents
29-4 Ampere’s Law 29-6 A Current-Carrying Coil as a
Magnetic Dipole
3
Fact: When a current flows
through a wire, it can produce a magnetic field.
For long (infinite) straight wire
carrying a current i,
i B R
Perpendicular distance
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Wrap your right hand around the wire with your thumb in the direction of the current. The fingers reveal the field vector’s direction, which is tangent to a circle.
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Computer cables, or cables for audio-video
equipment, create little or no magnetic field.
This is because within each cable,
closely spaced wires carry current in both directions along the length of the cable. The magnetic fields from these opposing currents cancel each other.
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Biot-Savart Law: The contribution 𝑒 𝐶 to the magnetic field produced by a current-length element 𝑗 𝑒 𝑡 at a point P located a distance r from the current element can be found by:
permeability constant = 4×10-7 T∙m/A 1.26×10-6 T∙m/A
2 2
ˆ 4 sin 4 i ds r dB r ids dB r
(experimentally deduced)
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To find the magnetic field produced at a point
Step 1: Find the contribution from each (single) current-
length element
Step 2: Integrate (superimposing/adding/summing the
contributions from all current-length elements) to find the net field produced by all the current-length elements.
2
ˆ 4 i ds r dB r B dB
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2 2 2 3 3 2 2 2 2
sin( ) 4 sin( ) 2 4 4 1 1 2 2 1 2 2 i ds dB r i i R r B ds ds r r iR iR ds ds r s R iR i R R
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Consider a wire consists of two straight sections (1 and 2)
and a circular arc (3), and carries current i.
What magnetic field (magnitude and direction) does the
current produce at C?
For now, focus on the two straight sections (1 and 2).
Their extensions intersect the center C of the arc.
Conclusion: Current directly toward or away from C does not create any magnetic field there.
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Consider only point P at the center of the arc (point C)
2 2 2
sin(90 ) 4 4 4 4 i ds i ds i R d dB r R R i B R
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Consider a wire consists of two straight sections (1 and 2)
and a circular arc (3), and carries current i.
What magnetic field (magnitude and direction) does the
current produce at C?
1 2 4 8 i i B R R
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Consider point P on the central perpendicular axis of the loop
2 3 2 2 2
2
B R z A Current-Carrying Coil as a Magnetic Dipole: Observation: One side of the loop acts as a north pole and the other side as a south pole, as suggested by the lightly drawn magnet.
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From the symmetry, the vector sum of all the perpendicular components due to all the loop elements is zero.
2 2
sin 90 4 4 i ds i dB ds r r
// 3 2 2 2 3 2
cos cos 4 4 4 i d dB iR iR ds ds r R z B ds r
3 2 2 2 // 3 3 2 2 2 2 2 2 2
2 4 4 2 i iR R z R iR B dB ds R R z R z
cos R r
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Two long parallel wires carrying currents exert forces on
each other.
sin 90 2 2
a a b ba b a b
i Li i F i LB i L d d
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Two long parallel wires carrying currents exert forces on
each other.
Two wires with parallel
currents attract each other.
Two wires with antiparallel
currents repel each other.
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Basis for the definition of ampere
The ampere is that constant current which, if maintained in
two straight, parallel conductors of infinite length, of negligible circular cross section, and placed 1 m apart in vacuum, would produce on each of these conductors a force of magnitude 2×10-7 N/m of wire length.
Rail gun
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Three long straight parallel equally-spaced wires with
identical currents either into or out of the page.
Rank the wires according to the magnitude of the force on
each due to the currents in the other two wires, greatest first.
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Net magnetic field
due to the three currents:
𝑪
i1 i2 i3
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0 enc
B ds i
Net current encircled by (passing through) the loop cos d B s The field component tangent to the loop
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Use the curled–straight right-hand
rule to determine the signs for currents
May have to integrate the current
density.
For conducting cylinder,
enc
i J dA
1 2 enc
i i i
2
enc
i J r r dr
Remark: The integration is over the area encircled by the loop.
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Use one that create symmetry. Draw the loop so that 𝐶cos𝜄 is constant. In which case, cos B ds B ds
In addition, if the magnetic field is always tangent to the loop
B ds B ds
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B outside: B inside:
With uniformly distributed current,
2 2 B r B ds i i B r
2 2 2
2 2 r B r B ds i R i r B R
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Magnetic fields are associated with a signal-carrying coaxial cable. If the current is the same magnitude in each direction, the
magnetic field outside the coaxial cable is zero.
The absence of
𝐶 fields around a coaxial cable results in no interference in nearby electrical equipment and wires
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A solenoid carrying current i. A vertical cross section through the central axis of a “stretched-out” solenoid.
The field inside the coil is fairly
strong and uniform over the cross section of the coil.
At points inside and reasonably far
from the wire, 𝐶 is approximately parallel to the (central) solenoid axis.
The external field, however, is
relatively weak.
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Infinitely long Consist of tightly packed (close-packed) turns of square wire The magnetic field outside the solenoid is zero. This is practically holds for real solenoid if
its length is much greater than its diameter we consider points that are well away from the solenoid ends
0 enc
B ds i
i h Bh B n n i
#turns per unit length
1
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B L
d dt di L dt
2
Principles of Physics Ninth Edition, International Student Version David Halliday, Robert Resnick,
and Jearl Walker
Chapter 30
30-2 Two Experiments 30-3 Faraday’s Law of Induction 30-4 Lenz’s Law 30-7 Inductors and Inductance 30-8 Self-Induction 30-9 RL Circuits
3
Review
Force occurs when a charged particle moves through a magnetic
field.
Force occurs when a current-carrying wire is placed in a
magnetic field.
Magnetic field is found around a current-carrying wire.
New Fact: Change in magnetic field can produce
(induce) a current in a loop of wire
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TMS = Transcranial Magnetic Stimulation A technique for studying (or stimulating or deactivating
(suppressing)) the function of various parts of the brain.
A coil held to the subject’s head carries a varying electric
current, and so produces a varying magnetic field. This field causes an induced emf, and that triggers electric activity in the region of the brain underneath the coil.
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Moving a magnet bar toward or away from a (conducting) loop
The current produced in the loop is called an induced current. Observation:
Current only occurs when there is a
relative motion between the loop and the magnet.
Faster motion produces a greater
current
Direction (CW or CCW) of the
(induced) current depends on the direction of motion and polarity of the magnet.
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When the switch is suddenly closed (i.e. current flows
through the right-hand loop) the ammeter will show a brief current appearing in the left-hand loop.
When the switch is suddenly
through the right-hand loop) the ammeter will again show a brief current appearing in the left-hand loop, but in the
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The current produced in the loop is called an induced
current.
The work done per unit charge to produce that current (to
move the conduction electrons that constitute the current) is called an induced emf.
The process of producing the current and emf is called
induction.
Faraday’s law of induction:
An emf is induced in a loop when the amount of magnetic field that passes through the loop is changing.
(number of magnetic field line)
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Need to quantify the amount of magnetic field that passes
through the loop
Magnetic flux through a loop enclosing an area A Unit: weber (Wb)
1 weber = 1 Wb = 1 T·m2
B
d B A
Vector of magnitude dA that is perpendicular to a differential area dA Dot product
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Here are the general means by which we can change the magnetic flux through a coil:
Change the magnitude B of the magnetic field within the
coil.
Change either the total area of the coil or the portion of that
area that lies within the magnetic field (for example, by expanding the coil or sliding it into or out of the field).
Change the angle between the direction of the magnetic field
𝐶 and the plane of the coil (for example, by rotating the coil so that field 𝐶 is first perpendicular to the plane of the coil and then is along that plane).
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The magnitude of the emf induced in a conducting loop is equal to
the rate at which the magnetic flux 𝛸𝐶 through the loop changes with time.
The negative sign is there because the induced emf tends to
If we change the magnetic flux through a coil of N turns, an
induced emf appears in every turn and the total emf induced in the coil is the sum of these individual induced emfs
B
d dt
B
d N dt
Assume that the coil is tightly wound (closely packed), so that the same magnetic flux passes through all the turns.
10
The graph gives the magnitude B(t) of a uniform magnetic
field that exists throughout a conducting loop,with the direction of the field perpendicular to the plane of the loop.
Rank the five regions of the graph according to the
magnitude of the emf induced in the loop, greatest first.
11
A long solenoid has 220 turns/cm and carries a current i
=1.5 A; its diameter D is 3.2 cm.
At the center we place a 130 turn closely packed coil C of
diameter d = 2.1 cm. The current in the long solenoid is reduced to zero at a constant rate in 25 ms.
What is the magnitude of the induced emf in coil C?
12
“An induced current has a direction
such that the magnetic field due to the current opposes the change in the magnetic flux that induces the current.”
13
Note carefully that the flux of 𝐶
𝑗𝑜𝑒 always opposes the change in the flux of 𝐶
. Does not mean that 𝐶
𝑗𝑜𝑒 always points opposite 𝐶
.
14
Consider a conducting loop consisting of a half-circle of radius r
= 0.20 m and three straight sections. The half-circle lies in a uniform magnetic field that is directed out of the page; the field magnitude is given by B = 4.0t2 +2.0t + 3.0, with B in teslas and t in seconds.
An ideal battery with emf ℰ𝑐𝑏𝑢
= 2.0 V is connected to the loop.
The resistance of the loop is 2.0
Ω
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r = 0.20 m, B = 4.0t2 +2.0t + 3.0, ℰ𝑐𝑏𝑢 = 2.0 V
, R = 2.0 Ω
a)
What are the magnitude and direction of the emf ℰ𝑗𝑜𝑒 induced around the loop by field 𝐶 at t = 10 s?
b)
What is the current in the loop at t = 10 s?
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An induced emf appears in any coil in which the current is
changing.
This process is called self-induction. The emf that appears is called a self-induced emf. Still obeys Faraday’s law
and Lenz’s law.
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An inductor is an electrical component
typically made by coiling a conductor around a core.
Solenoid is our basic type of inductor.
The inductance of the inductor is Unit: henry
1 henry = 1 H = 1 T∙m2/A.
B
N L i
the number of turns
solenoid 2 B N
n in A L i n A
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Let’s combine self induction and inductance. In any inductor (such as a solenoid) a self-induced emf
appears whenever the current changes with time.
The direction can be obtained by Lenz’s law. For an ideal inductor with negligible resistance, the
magnitude of the potential difference VL across the inductor is equal to the magnitude of the self-induced emf ℰ𝑀.
B B L
d d d di N L dt d N Li t dt dt
Faraday’s law
Inductance
B
N L i
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Kirchhoff’s voltage law
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Consider a circuit that contains three identical resistors with
resistance R = 9.0 , two identical inductors with inductance L = 2.0 mH, and an ideal battery with emf ℰ = 18 V .
What is the current i through the battery just after the switch
is closed?
21
What is the current i through the battery long after the
switch has been closed?
1
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R R C C L L
v i R dv i C dt di v L dt
2
Principles of Physics Ninth Edition, International Student Version David Halliday, Robert Resnick,
and JearlWalker
Chapter 31
31-6 Alternating Current 31-7 Forced Oscillations 31-8 Three Simple Circuits
3
A conducting loop rotates (with constant angular speed ) in
an external (uniform and constant) magnetic field.
Connections from each end of the loop to the external
circuit are made by means of that end’s slip ring.
4
A sinusoid (or sinusoidal signal) is a signal (e.g. voltage or
current) that has the form of the sine or cosine function.
Turn out that you can express them all under the same notation
using only cosine (or only sine) function.
We will use cosine.
A sinusoidal current is referred to as alternating current
(ac).
Circuits driven by sinusoidal (current or voltage) sources are
called ac circuits.
We use the term ac source for any device that supplies a
sinusoidally varying voltage (potential difference) or current
The usual circuit-diagram symbol for an ac source is
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General sinusoidal signal (in cosine form) Xm: amplitude of the sinusoid
Nonnegative when expressed in standard form
T: period (the time of one complete cycle) f: frequency
#cycles per second
ω: angular frequency in radians/s (or rad/s) 𝜚: phase
Between −180◦and +180◦ in standard form
( ) cos( ) cos(2 ).
m m
x t X t X ft 1 2 f T
6
Japan: 100 V; 50 Hz (East), 60 Hz (West) Thailand: 220 V; 50 Hz US: 120 V; 60 Hz
7
When the signal is given in the sine form, it can be converted
into its cosine form via the identity
In particular,
We can avoid having Xm with negative sign by the following
conversion:
In particular,
Note that usually you do not have the choice between +180◦or
−180◦. The one that you need to use is the one that makes 𝜚±180◦ falls somewhere between −180◦and +180◦.
sin( ) cos( 90 ). x x sin( ) cos( 90 ).
m m
X t X t cos( ) cos( 180 ). x x cos( ) cos(2 180 ). A t A ft
8
Express the following sinusoids in their standard forms
5cos 2 45 5sin 2 45 5cos 2 45 5sin 2 45 t t t t
9
10 5 5 10 6 4 2 2 4 6 5 cos 2 t ( ) t 10 5 5 10 6 4 2 2 4 6 5 cos 2 t 45 deg ( ) t 10 5 5 10 6 4 2 2 4 6 5 cos 2 t 45 deg ( ) 5 cos 2 t 135 deg ( ) t 10 5 5 10 6 4 2 2 4 6 5 sin 2 t 45 deg ( ) 5 cos 2 t 135 deg ( ) t 10 5 5 10 6 4 2 2 4 6 5 sin 2 t 45 deg ( ) 5 cos 2 t 45 deg ( ) t
10
The electrodes attached to this
applying a small ac voltage of frequency 50 kHz.
The attached instrumentation
measures the amplitude and phase angle of the resulting current through the patient’s body.
These depend on the relative
amounts of water and fat along the path followed by the current, and so provide a sensitive measure of body composition.
1
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2
Principles of Physics Ninth Edition, International Student Version David Halliday, Robert Resnick,
and JearlWalker
Chapter 32
32-2 Gauss’ Law for Magnetic Fields 32-3 Induced Magnetic Fields 32-5 Maxwell’s Equations
Chapter 33
33-2 Maxwell’s Rainbow 33-3 The Traveling Electromagnetic
Wave, Qualitatively
3
GLE: Gauss’s Law for Electric Fields: The net electric
flux through a closed Gaussian surface is proportional to the net electric charge qenc enclosed by the surface.
GLB: Gauss’s Law for Magnetic Fields:
Net magnetic flux through any closed Gaussian surface is zero.
B
B dA
enc E
q E dA
Integrals are taken over a closed Gaussian surface
4
Magnetic monopoles (single magnetic poles) do
not exist (as far as we know).
The simplest magnetic structure that can exist is a
magnetic dipole
which consists of both a source and a sink for the field
lines.
Thus, there must always be as much magnetic flux into
the surface as out of it, and the net magnetic flux must always be zero.
If you break a magnet, each fragment becomes a
separate magnet, with its own north and south poles.
Even if we break the magnet down to its individual
atoms and then to its electrons and nuclei. Each fragment still has a north pole and a south pole.
5
Faraday’s law of induction: A changing magnetic flux
induces an electric field.
Maxwell’s law of induction: A changing electric flux
induces a magnetic field.
B
d dt
B
d E ds dt
E
d B ds dt
Electric field induced along a closed loop by the changing magnetic flux encircled by that loop. Magnetic field induced along a closed loop by the changing electric flux in the region encircled by that loop.
6
Magnetic field is produced by a current and/or by a changing electric field:
0 enc
B ds i
E
dt d d B s
d,e nc enc en E c
i d d i s dt B i
Displacement current (id)
Maxwell’s Law of Induction (Maxwell’s Extension of Ampere’s Law) Ampere’s Law
7
Maxwell’s equations, displayed below summarize electromagnetism and form its foundation, including optics.
James Clerk Maxwell (1831–1879) was the first person to truly understand the fundamental nature of light. Einstein described Maxwell’s accomplishments as “the most profound and the most fruitful that physics has experienced since the time of Newton.”
8
that changed the world … and still rule everyday life
9
10
Do not require material medium. Can travel across empty space. The magnetic field varies sinusoidally and induces (via Faraday’s
law of induction) a perpendicular electric field that also varies sinusoidally.
Electric field is varying sinusoidally and induces (via Maxwell’s law
sinusoidally.
And so on. The two fields continuously create each other via induction, and
the resulting sinusoidal variations in the fields travel as a electromagnetic wave.
11
Transverse wave:
𝐹and 𝐶 are always perpendicular to the direction in which the wave travels.
𝐹 is always perpendicular to 𝐶.
The cross product,
𝐹 𝐶 gives the direction of propagation.
snapshot
12
The
𝐹and 𝐶 fields vary with the same frequency and in-phase with each other.
For an EM wave that is assume that is traveling positive direction
𝐹 oscillating parallel to the y axis, and 𝐶
cos( ) cos( )
m m
E E kx t B B kx t
amplitudes of the fields angular frequency angular wave number Electric wave component Magnetic wave component
1
m m
E E c k B B
Wave speed amplitude ratio magnitude ratio The meter has now been defined so that the speed of light (any EM wave) in vacuum has the exact value c = 299 792 458 m/s,
13
We now know a wide spectrum (or range) of electromagnetic
(EM) waves.
Certain regions are identified by familiar labels. These labels
denote roughly defined wavelength ranges within which certain kinds of sources and detectors
in common use.
14
Many insects and birds can see ultraviolet wavelengths that
humans cannot.
[http://www.nature.com/scitable/blog/the-artful-brain/alternate_realities]
UV Vision (bright = UV). The center target is vastly larger than the version we see. Also observe a faint UV glow in the center Simulated (red- blind) bee vision (UV+G+B) Some species, such as birds, along with most reptiles, have four types
(UV+R+G+B) [Dr.Klaus Schmitt] Human vision
15
Gazania flower shot using white light Gazania flower shot using ultraviolet light to make
16
Many birds with ultraviolet vision have ultraviolet patterns on their bodies that
make them even more vivid to each other than they appear to us.
Ultraviolet reflecting plumage in starlings had profound effects on observed
mating preferences, while plumage in the human visible spectrum did not predict choice. Their ultraviolet feathers are part of their mating call!
17
[Gosling , 1999, Fig 1.1 and 1.2]
c f
Wavelength Frequency
8
3 10 m/s
18
Commercially exploited bands
c f
Wavelength Frequency
8
3 10 m/s
[http://www.britannica.com/EBchecked/topic-art/585825/3697/Commercially-exploited-bands-of-the-radio-frequency-spectrum]
Note that the freq. bands are given in decades; the VHF band has 10 times as much frequency space as the HF band.
19
Spectral resource is limited. Most countries have government agencies responsible for
allocating and controlling the use of the radio spectrum.
Commercial spectral allocation is governed
globally by the International Telecommunications Union (ITU)
ITU Radiocommunication Sector (ITU-R) is responsible for radio
communication. in the U.S. by the Federal Communications Commission (FCC) in Europe by the European Telecommunications Standards Institute
(ETSI)
in Thailand by the National Broadcasting and Telecommunications
Commission (NBTC; คณะกรรมการกิจการกระจายเสียง กิจการโทรทัศน์และกิจการ โทรคมนาคมแห่งชาติ ; กสทช.)
Blocks of spectrum are now commonly assigned through spectral
auctions to the highest bidder.
20
21
http://www.ntc.or.th/uploadfiles/freq_chart_thai.htm
22
4.5bn baht per license (freq chunk)
1 license (chunk) = 5 MHz (UL) + 5 MHz (DL) 450 million baht per MHz 30 million baht per MHz per year
23
GPS = Global Positioning System Original application in the (US) military Created in the early 1990s. Allow a person to determine the time and the person's
precise location (latitude, longitude, and altitude) anywhere
24
A minimum of 24 GPS satellites are in orbit at 20,200
kilometers (12,600 miles) above the Earth.
The satellites are spaced so that from any point on Earth, at
least four satellites will be above the horizon.
25
A GPS receiver measuring its distance from a group of
satellites in space which are acting as precise reference points.
All the satellites have atomic clocks of unbelievable precision on
board and are synchronized.
The satellite are continuously transmitting the information about
their location and time.
GPS receiver on the ground is in synchronism with the satellites.
Off by an (unknown) amount . For now, assume = 0.
By measuring the propagation time, the receiver can compute
distance d from that satellite.
26
Intersection of three sphere narrows down the location to
just two points.
In practice, there are four unknowns, the coordinates in the
three-dimensional space of the user along with within the user’s receiver.
Need a distance measurement from a fourth satellite.
[Lathi ,1998, Fig. 9.6 ]