Download Topic #21, Magnetic Fields and Magnetic Phenomenon

Topic #21, Magnetic Fields and Magnetic Phenomenon
Part I: Magnetic Fields
1. General Properties of Magnets
2. Magnetic Fields Around Permanent Magnets
3. Electromagnetism
4. Magnetic Field Around a Coil
5. Forces on Currents in Magnetic Fields
6. Measuring the Force on a Wire (not printed in notes)
7. Galvanometers
8. Electric Motors
9. The Force on a single Charged Particle (Optional / not printed in the passage)
Part II: Electromagnetic Induction
1. Faraday's Discovery
2. Induced EMF
3. Electric Generators
4. Alternating-Current Generators
5. Generators and Motors
6. Lenz's Law
7. Self-Inductance
8. Transformers
Notes Should Include:
Special Note: It is said that Benjamin Franklin, who was a scientist as well as a statesman and a
publisher, defined electricity as the flow of positive charge. This occurred long before the
discovery of the electron or any other subatomic particle. It turns out that it is the electron, the
negatively charged particle, that actually moves when electric current flows. On the other hand,
the applications of the principles and equations to the study of magnetism work just fine using
either definition. This is important to know when you study the relationship between electricity
and magnetism. In the following passage you will encounter several left hand rules based upon
actual movement of electrons through wires. There is a counterpart to all of this when describing
electricity as the flow of positive charge. First of all electric current is called “conventional
current” when the current is defined as the flow of positive charge. Second of all the left hand
rules referred to here are redefined as right hand rules. You may be expected to know both.
Part I: Magnetic Fields
General Properties of Magnets: Naturally occurring magnetic rocks are called lodestones.
Though these rocks were known about more than 2,000 years ago, and were used for navigation
once it was realized that they aligned themselves with the north and south directions, it wasn't
until the beginning of the 17th century that an investigation was carried out on magnets and
magnetic phenomenon. A person by the name of William Gilbert conducted this research. The
properties of naturally occurring and artificial magnets (magnets produced by magnetizing
material which was not previously magnetized) are discussed here.
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Characteristic Properties: First - magnets have polarity. The end that points north is often
referred to as the north seeking end of the magnet or what is frequently called the north pole of
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the magnet. Likewise, the end that points towards the south is called the south seeking end of the
magnet or the south pole of the magnet. Though these poles are distinct (very different from one
another), they cannot be separated from each other. A magnet cannot just have a north pole or a
south pole by itself. This has to do with the nature of magnetism. Second - Like magnetic poles,
as in two north or two south poles, repel one another while unlike magnetic poles attract each
other. Third - A compass is a small needle shaped magnet that is suspended so it can turn freely
without any significant amount of friction. The end of the magnet pointing towards the north is
not actually pointing towards the geographical north (the north pole of the earths axis), but rather
is pointing towards the earth's magnetic north pole. In recent years the north magnetic pole has
been in northern part of Canada not far from the Arctic Circle, but it may not remain there. The
magnetic poles drift over the course of time. The poles can move around considerably each day,
but migrates on average about 10 kilometers to 40 kilometers each year. Fourth - The materials
that show magnetic properties are Iron, Nickel, and Cobalt. Permanent magnets are made of
alloys of these materials. A magnet made for commercial sale is often made out of an alloy of
aluminum, nickel, cobalt, and iron called ALNICO. Permanent magnets retain their magnetism
for a long time. Fifth - Iron, Cobalt, and Nickel can be magnetized by induction. Bringing a piece
of iron into contact with a permanent magnet will cause the iron to become a temporary magnet.
Remove the permanent magnet and the piece of iron loses most if not all of the magnetism. Some
residual magnetism may remain.
Magnetic Fields Around Permanent Magnets: Magnets, like mass and charge, exert force over
distance. This means that a magnet has a field around it that can affect other objects with
magnetic properties. If another object, a magnet or a material that responds to a magnet, is
brought into this field at some specified distance, there will be either a force of attraction or
repulsion between the original magnet and the object. This region around the magnet is called a
magnetic field. The magnetic fields around magnets can be made visible by placing a sheet of
paper over the magnet and then sprinkling iron filings over the piece of paper. The magnetic field
will align the filings along the magnetic field. The pattern looks like lines because the particles
are long and thin. Often these lines are called magnetic field lines. You should remember that
these lines are just a model used to visualize the invisible field and are not the field itself, though
for convenience it may be convenient to discuss the field as though it were made up of the lines.
For example, there is a measurement called the magnetic flux. The magnetic flux measures the
number of magnetic field lines in any given location within a magnet's magnetic field. It follows
that the flux per unit cross sectional area is a means of describing the strength of the magnetic
field at that location.
If you made a sketch of a magnet such as a bar magnet and included the magnetic field lines, it
would be appropriate to place arrows on the lines to show the direction of the field. The field
lines would appear to move out from the north pole of the magnet and curve around to the south
pole of the magnet. All of the lines arriving at the south pole of the magnet would go straight up
the magnet to the north pole of the magnet where they would again move out and curve back
towards the south pole of the magnet. One limitation of such a diagram is that it is only twodimensional and therefore only shows the lines in one plane. The actual field and therefore the
lines that represent it would best be shown as a three dimensional image.
Electromagnetism: Back around 1820, a Danish scientist by the name of Hans Christian
Oersted, discovered that electric current affects magnets. He laid a current carrying wire across a
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compass and observed that the needle was deflected when the current flowed, but returned to its
normal north - south orientation when the current was turned off. He deduced that the current
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was producing a magnetic field. This field can be visualized using iron filings. Attach a wide
cardboard collar around a wire. Set the wire up vertically and make the collar perpendicular to it.
Shake some iron filings onto the collar and run a current through the wire. What you would see is
the alignment of the filings forming a circular line around the wire. The filings are aligning
themselves in the magnetic field produced by the electrical charges flowing through the wire. The
pattern observed shows us that the magnetic field lines form “closed circles” (loops) around the
wire. The larger the current flowing through the wire the larger the magnetic field formed around
the wire. The strength of the magnetic field drops off with the square of the distance from the
wire. To find the direction of the magnetic field around the wire (i.e. clockwise or
counterclockwise from your perspective) use the first left - hand rule.
The left hand rule says to grasp the wire in your left hand with your thumb pointing in the
direction of the electron flow. The fingers of you hand point in the direction of the magnetic field.
If you were describing electric current as the flow of positive charge (perceived as flowing in the
opposite direction to the electrons) you would use the right hand and it would be called the right hand rule. In either case the direction of the magnetic field is the same around the wire.
A Magnetic Field Around a Coil: An interesting phenomenon occurs when a wire is formed
into a circle (loop) at some point in a circuit. A magnetic field will appear all around the loop
when a current flows through the wire. The left - hand rule will show what direction the magnetic
field is pointing in terms of the plane the loop lies in. For an example, consider a loop of wire
lying in a horizontal plane in front of you. The wire feeds electrons into and out of the loop so as
you look down on the loop the current is flowing clockwise around the loop. Applying the left hand rule you would discover that the magnetic field points up out of the plane the loop is in.
Inside this single coil (loop) there is a continuous magnetic field pointing upwards. Outside the
coil the field acts in a downward direction. The coil acts like a permanent magnet with one side of
the coil (the top side in this case) acting as the north pole of the magnet and the other side of the
coil (the bottom side in this case) acting as a south pole of the magnet. Bring a north pole of a
permanent magnet near the north pole of this coil (loop) and it would be repelled. Bring a south
pole of a permanent magnet near the north pole of this coil and it would be attracted.
A current carrying wire can be looped a number of times rather than just once. Technically, a coil
is not a single loop, though you might call it that. A coil consists of more than one loop. A coil
having a magnetic field produced by a current traveling through the wire making up the coil is
called an electromagnet. The magnetic field’s direction in a coil of wire can be found by the use
of the second left - hand rule.
The second left-hand rule says to grasp the coil with your left hand so that your finger wrap
around the loops of the coil in the direction the current is traveling through the wires that make up
the loops in the coil. Your thumb will point in the direction of the north pole of the coil
(electromagnet). The strength of the electromagnet field can be increased when an iron rod, often
called a core, is placed inside the coil. This core is magnetized by induction and its magnetic field
combines with the coils magnetic field to produce a stronger field. Increasing the number of loops
in a coil also increases the strength of the magnetic field produced by the electromagnet.
Magnetic Materials: Around the turn of the 18th century, a scientist by the name of Andre
Ampere suggested that magnetism in magnets was due to little "loops of current" existing within
the bar. It appears that he knew something of the nature of electromagnetism and concluded that
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there must be a similar phenomenon happening within the structure of materials which exhibited
magnetic characteristics. Based upon what we know about the atom's structure and how that
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structure helps us to explain magnetic phenomenon, he was essentially correct, though not very
technical, because atomic structure wasn't even known about yet, much less understood.
In the atom the electrons move about the nucleus. These electrons also spin. Each electron, in
effect, acts like a very tiny magnet. (remember that moving charge produces magnetic fields) It is
possible for the electrons' magnetic fields to combine making for even a larger and stronger field.
This can happen among neighboring atoms in some materials. These clusters of atoms
collectively producing a magnetic field are called domains. Even though these domains may
consist of hundreds of atoms, domains are quite small compared to even the smallest magnet that
you can see and hold in your hand. If these domains in a material like iron point off in many
different directions, the piece of metal as a whole does not exhibit any significant magnetic
properties. However, if the domains can be made to line up so their individual magnetic fields
reinforce each other, the piece of iron exhibits magnetic properties and acts as a magnet. In a
temporary magnet enough domains line up as long as the material is in a strong magnetic field.
Fairly soon after the magnetic field is cut off or moved away from the temporary magnet, its
domains shift back to their random patterns as before being exposed to the field. In permanent
magnets the iron is alloyed with other materials that contribute to keeping the domains aligned.
Forces on Currents in Magnetic Fields: Andre Ampere also hypothesized that a magnetic field
should exert a force on a wire that had a current flowing through it. The strength of a magnetic
field is called magnetic induction (Symbol B). A scientist by the name of Michael Faraday,
during the first half of the 19th century, determined that the force on the wire caused by the
magnetic is at right angles to the magnetic field. The force is also at right angles to the direction
of the current as well. The direction of the force is determined through the third left - hand rule.
This rule is used when the current carrying wire is placed between the two poles of a magnet.
This rule says to point the fingers of the left hand in the direction of the magnetic field. Then
point the thumb in the direction of the current flow. Finally, the palm of the hand faces in the
direction of the force acting on moving the wire.
Galvanometers: The galvanometer is a device used to measure very small currents and is found
in many voltmeters and ammeters. Structurally, the galvanometer has coil of wire placed in the
magnetic field of a strong magnet. When current flows through the coil it rotates in the magnetic
field. According to the third left - hand rule one side of the coil is pressed down while the other
side is of the loop is forced up. The loop is sitting on a shaft that allows it to rotate, and when
current is flowing through the coil it does rotate. The more current in the loop the further it turns.
The force on the coil varies directly with the current traveling through the coil. The turning coil is
working against a small spring, which if current is not present would pull the coil back to a
starting position. A needle pointing to a scale moves across the scale indicating the amount of
current flowing through the coil. The scale is calibrated by using known amounts of currents so
values can be printed up on the scale.
When the galvanometer is used as an ammeter a resistor is placed in parallel to the circuit having
the coil. This resistor is kept small and acts as a shunt for most of the current that would be
blocked by the resistance of the main galvanometer circuit. The meter is sensitive to small
currents so very little needs to pass through the coil to get a measurement of current in the
electrical circuit the ammeter has been placed in. When the galvanometer is used as a voltmeter, a
resistor called a multiplier is placed in series with the galvanometer circuit. The meter is
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calibrated to read in volts, though the galvanometer measures the current passing through it. The
ammeter is wired in series with the path in which the current is flowing and its resistance must be
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low so the effective resistance of the circuit remains essentially unaffected. The voltmeter is
wired in parallel with the device whose voltage drop is being measured and its resistance must be
very high so little current passes through it changing the parameters of the circuit. Ammeters and
voltmeters should have very little if any impact on the circuit they are being used on, if the data
collected from the instruments is to mean much.
Electric Motors: The small coil in a galvanometer is limited to a maximum rotation of 180o. For
a loop to turn beyond 180o and be able to turn through 360o and so on, the current has to be able
be reversed so each 180 degrees the forces are in opposition. To allow the current to change
direction every 180 degrees a split ring commutator is used to connect the coil part of the circuit
with the source of the voltage. In simple terms half of the ring is attached to a wire connected to
one wire of the coil and the other half of the ring is attached to the other wire of the coil. Current
flows from a voltage source through a wire which has a brush (a sliding metal contact) which
touches one half of the ring and returns to the voltage source through the other half of the ring
which has a second brush touching it which in turn is connected to the second wire (the return
wire) that is connected to the voltage source.
Part II: Electromagnetic Induction
Faradays Discovery: Michael Faraday spent about ten years trying to produce a current in a
wire using magnetic fields of constant magnitude. Finally, he discovered that a changing
magnetic field could produce an electric current. He found that when he moved a wire through a
magnetic field an electric current was induced in the wire. If the wire was moved up through the
field, the current would flow in one direction and if the wire were moved down through the field
the current would flow in the opposite direction. If the wire is held stationary in the field, no
current flows through the wire. If the wire is moved parallel to the field, no current flows through
the wire. The wire has to "cut through" the field for an electric current to be produced.
Moving the field with respect to the wire while the wire remains stationary will also produce an
electric current as long as the motion still in effect causes the field to be "cut through" by the
wire. This method of producing electric current by causing a wire to move perpendicularly
through a magnetic field is called electromagnetic induction. If the wire in effect passes at an
angle through the field, neither moving parallel to the field (no current produced) nor moving
perpendicular to the field (current produced), only the portion of the wire's motion that is
perpendicular to the field will produce some current. This amount of current will be between zero
amperes and the amount that could be produced if the wire moved perpendicularly through the
field. To determine the direction of the current through the wire use the third left - hand rule. In
this case point the thumb in the direction the wire is moving and point the fingers in the direction
of the magnetic field. The palm of the hand points in the direction of the force pushing the
electrons, which is the direction the electrons will move, as in the direction current will flow.
Induced EMF: In a very real sense an electron pump is needed to make electrons move
(electricity). The potential difference (voltage) necessary to move the charges can be referred to
as the electromotive force (EMF). This, contrary to the name, is NOT a force, but is a
measurement of the electrical potential difference expressed in the units volts. Think of electrical
potential as being similar to gravitational potential energy. The water at the top of a water fall has
potential energy. When the water is not being blocked by the use of a dam, it will flow, and as it
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does its potential energy becomes kinetic energy. If the water is dammed up and stored in a
reservoir waiting to flow through a channel, it retains its potential energy until it is allowed to
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flow. Similarly a fully charged battery is an electrical reservoir full of charge waiting to flow
through a circuit. When a wire is moved through a magnetic field, the electrons experience an
increase in energy. In effect, they experience an increase in electrical potential. This increase in
electrical potential is the called the induced EMF, and is expressed in volts. When the wire was
stationary its EMF was zero. The EMF the wire experiences is a function of the magnetic
induction, the length of wire in the field, and the velocity of the wire in the field. Producing an
EMF doesn't mean that a current will automatically flow through the wire. The wire needs to be
part of a circuit for current to actually flow. This is similar to a battery. It too has electrical
potential when charged, but no current flows either from it or into it, unless it is part of a circuit.
Electric Generators: Michael Faraday is credited with inventing the electric generator. An
electric generator has a coil of wire loops placed in a magnetic field. A mechanical device is
attached to a shaft that the coil is mounted on. As the coil is turned by a crank or even a steam
turbine (used in electrical generating plants) current is produced in the wire loops of the coil. The
wire loops in the coil are sometimes called windings and the windings mounted on a shaft are
called an armature. The coil of loops mounted on a shaft in an electric motor is also called an
armature. The wire in these windings must have a thin but strong insulation around them, so no
current jumps between the loops causing a short circuit. As the armature in the generator is
turned, the moving loops of wire in the rotating coil cause the EMF to fluctuate from zero (where
the loop is moving parallel to the field) to a maximum value (where the loop is moving exactly
perpendicular to the field).
This process happens twice during one 360o rotation. Within the first 180 degrees the EMF goes
between zero and a maximum value causing current to rise and fall in one direction proportional
to the EMF value. Within the second 180 degrees The EMF again goes from zero to a maximum,
but the EMF is in the opposite direction, causing the current to rise and fall in the opposite
direction proportional to the EMF value. So for each turn of the crank, there are two current
spikes, one occurring during the first half of a turn and the other occurring during the second half
of the turn. The two current spikes however are in opposite directions, so what you have is
alternating current not direct current. The actual increase and decrease of current during one half
of a turn is not really sudden as the term spike might suggest, but rather a smooth increase and
decrease. A graph of the rise and fall of the current is cyclical and resembles a sign curve. As the
armature turns the angle keeps changing and the EMF (voltage) and the current (amperage) are
changed proportionally with each other.
Alternating Current Generator: In the United States one cycle of armature rotation has a
period of 1/60 of a second and the frequency is 60 hertz. This means that since each cycle of the
armature causes the current to flow first in one direction and then in the opposite direction, the
current changes direction 120 times each second. One wire from the armature coil connects to a
slip (not split, as in an electric motor) ring on the shaft. A brush attached to a wire from the rest of
the circuit makes contact with this ring. The other wire from the windings is attached to a second
slip ring also mounted on the shaft of the armature. A second brush attached this second wire
coming from the circuit makes contact with this second ring. When all contact points are closed
(touching without any breaks in the circuit, including a closed switch) current flows from the
generator through circuit and back. Of course the direction of this current is constantly reversing
itself. If there is not a continuous circuit for current to flow through the rotation of the armature
will still produce an oscillating EMF, but no current will be able to flow.
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Generators and Motors: Generators and motors are of similar construction. In the motor,
current is sent into the wire loops in the coil of the armature to produce a repulsive force between
the magnetic field of the magnet and the magnetic field produced in the loops of wire in the coil.
The opposing forces caused the armature to turn producing mechanical energy. In the case of the
generator no current is sent into the wire loops in the coil of the armature. Instead mechanical
energy is used to turn the armature. When the wire loops in the coil of the armature rotate in the
magnetic field an oscillating EMF is produced. If the generator is connected to a circuit
alternating current flows through the circuit.
Lenz's Law: It is interesting to note that even though a current is produced in the wire loops on
the armature as the loops move through the magnetic field, the presence of the current in the wire
loops produce a magnetic field of their own. This field produces a force that opposes the motion
of the turning loops of wire. This force acts in the direction opposite that of the motion of the wire
and actually slows down the rotation. The direction of this force was determined by H. F. E. Lenz
in 1834. This observation is called Lenz's law, which says that the current induced in a direction
such that the magnetic effects produced by that current oppose the change in flux that induced the
current. The change in flux is being opposed not the flux itself. When the generator is producing
only a little current the opposing force is small, but when the generator is producing a large
amount of current the opposing force is large.
Electric motors experience this phenomenon as well. When a current carrying wire moves in a
magnetic field an EMF is produced. This EMF opposes the current flow and is called "Back
EMF". When an electric motor is first turned on, there is a large flow of current because of the
low resistance in the wire of the armature. As the motor starts turning the movement of the wires
across the magnetic field induces back EMF. This back EMF opposes the current flow. As a
consequence the current flowing through the motor is reduced. If a mechanical load is placed on
the motor (this means the motor is used to do work and not just sit there with its armature shaft
spinning) the load slows down the rotational speed of the wire. This means the wire loops in the
armature are now moving through the magnetic field at a slower rate and are producing less back
EMF. This results in an increase in the flow of current flows. Should the load be so great as to
stop the armature from turning at all, such as in the case of an electric saw's blade binding in a
piece of wood, the current flow can increase to such an extent that the wires will overheat melting
or burning up the insulation. This can result in a short circuit, blown fuse, and one damaged
motor.
The large current flow when a motor is first started can cause voltage drops across the wires that
bring electricity to the motor. Wires do have resistances and in certain circumstances the voltage
drops across these resistances can be significant. The wires, referred to here, are the wires in the
motor circuit that are outside of the motor itself. If an ordinary light bulb were wired in parallel
with a motor, it would be seen to dim when the motor is first turned on and brighten again once
the motor was up to speed. What is happening here is that there is no significant back EMF when
the motor is first turned on. As a consequence there is an initial surge in current affecting both the
voltage drop across the wires that feed current to the motor and the voltage drop across the motor.
Initially this results in a momentary current surge in the circuit containing the motor. Since the
resistance of the light bulb does not change in the parallel path, more current initially goes
through the branch with the motor and less through the path with the light bulb. Consequently the
bulb appears to dim when the motor is first turned on. As the motor picks up speed the back EMF
increases and the current through the motor’s path decreases and the current through the light
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bulb increases causing the bulb to brighten once again. See the explanation in terms of Ohm’s law
in the next paragraph.
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Ohm's law tells us that V = I R. So when I suddenly increases a lot even though R is small, V
will increase a lot to. As the back EMF slows the current down after start up, the voltage drop
decreases and current to the light and in turn its brightness returns to normal. Another interesting
phenomenon associated with this situation involves the turning off or unplugging the motor while
its running. The sudden loss in the electromagnetic field will produce a back EMF that will cause
a spark to jump across the switch or across from the plug to the outlet.
Self - Inductance: As a current in a coil changes, an induced EMF is produced in that coil. This
process is called self - inductance. The direction of this EMF is opposite to the current flow.
Therefore, this EMF is opposing the flow of current. This opposition to the flow of current
explains why the current flow when a switch is thrown is not instantly at a maximum value but
requires a short amount of time to be reached. Once the desired current is reached, the current
remains constant, the magnetic flux is constant, and the EMF is zero. It is most important to
remember that it the change in the magnetic flux that induces this EMF, not the magnetic flux
itself. A decrease in current will cause a decrease in the magnetic flux and an EMF will be
generated that opposes the decrease in the current. (Rem: Magnetic flux is a measure of the
strength of a magnetic field. This is true whether it’s the field around a permanent magnet or
current carrying wire. Flux lines, used to represent magnetic fields, are always closed loops.)
Transformers: A transformer is an electrical device that is used to either increase or decrease
alternating current voltages. This is an example of electromagnetic induction at work.
Structurally, a transformer consists of two electrical coils wound around the same iron core. One
of the coils is called the primary coil while the other is called the secondary coil. When an AC
voltage source called the primary voltage is connected to the primary coil, the alternating
(changing) current produces a varying magnetic flux caused by the continual flip flopping of
current direction. This varying magnetic flux is carried by means of the core to the secondary
coil. This varying flux in the secondary core induces a varying EMF. The effect is called mutual
inductance. This induced EMF in the secondary coils is called the secondary voltage. The
magnitude of this secondary voltage is dependent upon the ratio of turns between the secondary
and the primary coil. The equation to calculate the secondary voltage is written VS / VP = NS / NP.
In this equation V is representing voltage and N is representing the number of turns in the coil. It
should be noted that, if the secondary voltage is larger than the primary voltage the transformer is
called a step - up transformer, but if the secondary voltage is less than the primary voltage the
transformer is called a step - down transformer. Ideally the electric power delivered by the
secondary circuit is equal to the power used by the primary circuit. The equation representing this
relationship is based on P = V I and is written as VP IP = VS IS. Step up transformers are used at
the electrical generating plants to develop high voltages for the transmission lines, while step
down transformers are used at substations and on poles to get the voltage down to the value used
by homes and businesses. In your automobile the spark or ignition coil is designed to step up the
12 volts from your battery to thousands of volts in order to supply the power necessary to run that
small electric starter motor that cranks your gasoline engine until it starts. (It sure beats hand
cranking your engine like people had to do in early cars and trucks.)
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Vocabulary: Part I: polarized, magnetic field, magnetic flux, first left hand rule / first right hand
rule, solenoid, electromagnet, second left hand rule / second right hand rule, domain, third left
hand rule / third left hand rule, galvanometer, electric motor, armature; Part II: electromagnetic
induction, electromotive force, electric generator, Lenz’s Law, eddy current, self inductance,
transformer, primary coil, secondary coil, mutual inductance, step up transformer, step down
transformer
Skills to be learned:
Solve problems using the left (or right) hand rules
Solve problems involving transformers
Assignments:
Textbook: Read / Study / Learn about Magnetism and Its Applications
WB Exercise(s):
Activities: TBA
Resources:
This Handout and the Overhead and Board Notes discussed in class
Textbook: Chapters 23 and 25
WB Lessons and Problem Sets
www.physicsphenomena.com - “Magnetic Fields and Magnetic Phenomenon”
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