Faraday's Law of Electromagnetic Induction.docx

7/25/2019 Faraday's Law of Electromagnetic Induction.docx

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What Is Faradays Law of Induction?

Faradays Law of Induction describes how an electric current produces a magnetic field

and, conversely, how a changing magnetic field generates an electric current in a

conductor. English physicist Michael Faraday gets the credit for discovering magnetic

induction in 1!"# however, an $merican physicist, %oseph &enry, independently made

the same discovery about the same time, according to the University of Texas.

It is impossible to overstate the significance of Faradays discovery. Magnetic induction

ma'es possible the electric motors, generators and transformers that form the

foundation of modern technology. (y understanding and using induction, we have an

electric power grid and many of the things we plug into it.

Faraday)s law was later incorporated into the more comprehensive Ma*wells e+uations,

according to Michael ubson, a professor of physics at the -niversity of olorado

(oulder. Ma*wells e+uations were developed by /cottish physicist %ames ler'

Ma*well to e*plain the relationship between electricity and magnetism, essentially

uniting them into a single electromagnet force and describing electromagnetic

wavesthat ma'e up radio waves, visible light, and 0rays.

Electricity

Electric chargeis a fundamental property of matter, according to the Rochester

Institute of Technology. $lthough it is difficult to describe what it actually is, we are

+uite familiar with how it behaves and interacts with other charges and fields. 2heelectric field from a locali3ed point charge is relatively simple, according to /erif -ran, a

professor of physics at 4ittsburg /tate -niversity. &e describes it as radiating out

e+ually in all directions, li'e light from a bare light bulb, and decreasing in strength as

the inverse s+uare of the distance 516r27, in accordance with Coulombs Law.8hen

you move twice as far away, the field strength decreases to onefourth, and when you

move three times farther away, it decreases to oneninth.

4rotons have positive charge, while electrons have negative charge. &owever, protons

are mostly immobili3ed inside atomic nuclei, so the 9ob of carrying charge from one

place to another is handled by electrons. Electrons in a conducting material such as a

metal are largely free to move from one atom to another along their conduction bands,

which are the highest electron orbits. $ sufficient electromotive force 5emf7, or voltage,

produces a charge imbalance that can cause electrons move through a conductor from

a region of more negative charge to a region of more positive charge. 2his movement is

what we recogni3e as an electric current.
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Magnetism

In order to understand Faradays Law of Induction, it is important to have a basic

understanding of magnetic fields. ompared to the electric field, the magnetic field is

more comple*. 8hile positive and negative electric charges can e*ist separately,

magnetic poles always come in pairs : one north and one south, according to /an

%ose /tate -niversity. 2ypically, magnets of all si3es : from subatomic particles to

industrialsi3e magnets to planets and stars : are dipoles, meaning they each have two

poles. 8e call these poles north and south after the direction in which compass needles

point. Interestingly, since opposite poles attract, and li'e poles repel, the magnetic north

pole of the Earth is actually a south magnetic pole because it attracts the north poles of

compass needles.

$ magnetic field is often depicted as lines of magnetic ux. In the case of a bar

magnet, the flu* lines e*it from the north pole and curve around to reenter at the southpole. In this model, the number of flu* lines passing through a given surface in space

represents the flu* density, or the strength of the field. &owever, it should be noted that

this is only a model. $ magnetic field is smooth and continuous and does not actually

consist of discrete lines.

agnetic !el" lines from a bar magnet#
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Earths magnetic field produces a tremendous amount of magnetic flu*, but it is

dispersed over a huge volume of space. 2herefore, only a small amount of flu* passes

through a given area, resulting in a relatively wea' field. (y comparison, the flu* from a

refrigerator magnet is tiny compared to that of the Earth, but its field strength is many

times stronger at close range where its flu* lines are much more densely pac'ed.&owever, the field +uic'ly becomes much wea'er as you move away.

Induction

If we run an electric current through a wire, it will produce a magnetic field around the

wire. 2he direction of this magnetic field can be determined by the right$han" rule.

$ccording to the physics department at (uffalo /tate -niversity of ;ew


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In a current$carrying circular loo%& 'a( the right$han" rule gives the "irectionof the magnetic !el" insi"e an" outsi"e the loo%# 'b( ore "etaile" ma%%ingof the !el"& which is similar to that of a bar magnet#

If we run a current through a wire loop in a magnetic field, the interaction of these

magnetic fields will e*ert a twisting force, or tor+ue, on the loop causing it to rotate,

according to the Rochester Institute of Technology. &owever, it will only rotate so far

until the magnetic fields are aligned. If we want the loop to continue rotating, we have to

reverse the direction of the current, which will reverse the direction of the magnetic field

from the loop. 2he loop will then rotate 1" degrees until its field is aligned in the otherdirection. 2his is the basis for the electric motor.

onversely, if we rotate a wire loop in a magnetic field, the field will induce an electric

current in the wire. 2he direction of the current will reverse every half turn, producing

an alternating current. 2his is the basis for the electric generator. It should be noted

here that it is not the motion of the wire but rather the opening and closing of the loop

with respect to the direction of the field that induces the current. 8hen the loop is face

on to the field, the ma*imum amount of flu* passes through the loop. &owever, when

the loop is turned edgeon to the field, no flu* lines pass through the loop. It is this

change in the amount of flu* passing through the loop that induces the current.

$nother e*periment we can perform is to form a wire into a loop and connect the ends

to a sensitive current meter, or galvanometer. If we then push a bar magnet through the

loop, the needle in the galvanometer will move, indicating an induced current. &owever,

once we stop the motion of the magnet, the current returns to 3ero. 2he field from the

magnet will only induce a current when it is increasing or decreasing. If we pull the
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magnet bac' out, it will again induce a current in the wire, but this time it will be in the

opposite direction.

agnet in a wire loo% connecte" to a galvanometer#

If we were to put a light bulb in the circuit, it would dissipate electrical energy in the form

of light and heat, and we would feel resistance to the motion of the magnet as wemoved it in and out of the loop. In order to move the magnet, we have to do wor' that is

e+uivalent to the energy being used by the light bulb.

In yet another e*periment, we might construct two wire loops, connect the ends of one

to a battery with a switch, and connect the ends of the other loop to a galvanometer. If

we place the two loops close to each other in a facetoface orientation, and we turn on

the power to the first loop, the galvanometer connected to the second loop will indicate

an induced current and then +uic'ly return to 3ero.

8hat is happening here is that the current in the first loop produces a magnetic field,which in turn induces a current in the second loop, but only for an instant when the

magnetic field is changing. 8hen you turn off the switch, the meter will deflect

momentarily in the opposite direction. 2his is further indication that it is the change in

the intensity of the magnetic field, and not its strength or motion that induces the

current.


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2he e*planation for this is that a magnetic field causes electrons in a conductor to

move. 2his motion is what we 'now as electric current. Eventually, though, the electrons

reach a point where they are in e+uilibrium with the field, at which point they will stop

moving. 2hen when the field is removed or turned off, the electrons will flow bac' to

their original location, producing a current in the opposite direction.

-nli'e a gravitational or electric field, a magnetic dipole field is a more comple* !

dimensional structure that varies in strength and direction according to the location

where it is measured, so it re+uires calculus to describe it fully. &owever, we can

describe a simplified case of a uniform magnetic field : for e*ample, a very small

section of a very large field : as =B> BA, where =Bis the absolute value of the

magnetic flu*, Bis the strength of the field, and Ais a defined area through which the

field passes. onversely, in this case the strength of a magnetic field is the flu* per unit

area, or B> =B6A.

Faradays Law

;ow that we have a basic understanding of the magnetic field, we are ready to define

Faradays Law of Induction. It states that the induced voltage in a circuit is proportional

to the rate of change over time of the magnetic flu* through that circuit. In other words,

the faster the magnetic field changes, the greater will be the voltage in the circuit. 2he

direction of the change in the magnetic field determines the direction of the current.

8e can increase the voltage by increasing the number of loops in the circuit. 2he

induced voltage in a coil with two loops will be twice that with one loop, and with three

loops it will be triple. 2his is why real motors and generators typically have large

numbers of coils.

In theory, motors and generators are the same. If you turn a motor, it will generate

electricity, and applying voltage to a generator, it will cause it to turn. &owever, most real

motors and generators are optimi3ed for only one function.

Transformers

$nother important application of Faradays Law of Induction is the transformer,

invented by )i*ola Tesla. In this device, alternating current, which changes direction

many times per second, is sent through a coil wrapped around a magnetic core. 2his

produces a changing magnetic field in the core, which in turn induces a current in

second coil wrapped around a different part of the same magnetic core.
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Transformer "iagram

2he ratio of the number of turns in the coils determines the ratio of the voltage between

the input and output current. For instance, if we ta'e a transformer with 1"" turns on the

input side and ?" turns on the output side, and we input an alternating current at @@"

volts, the output will be 11" volts. $ccording to &yperphysics, a transformer cannotincrease power, which is the product of voltage and current, so if the voltage is raised,

the current is proportionally lowered and vice versa. In our e*ample, an input of @@"

volts at 1" amps, or @,@"" watts, would produce an output of 11" volts at @" amps,

again, @,@"" watts. In practice, transformers are never perfectly efficient, but a well

designed transformer typically has a power loss of only a few percent, according to

the University of Texas.

2ransformers ma'e possible the electric grid we depend on for our industrial and

technological society. rosscountry transmission lines operate at hundreds of

thousands of volts in order to transmit more power within the currentcarrying limits of

the wires. 2his voltage is stepped down repeatedly using transformers at distribution

substations until it reaches your house, where it is finally stepped down to @@" and 11"

volts that can run your electric stove and computer.
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Generators and Motors

Basic Magnetic FieldMagnets are pieces of metal that have the ability to attract other metals. Every magnet

has two polesA a north and a south. Much li'e electrical charges, two similar magneticpoles repel each other# while opposite magnetic poles attract each other. Magnets have

a continuous force around them that is 'nown as a magnetic field. 2his field enables

them to attract other metals. Figure 1 illustrates this force using bar and horseshoe

magnets.

2he shape of the magnet dictates the path the lines of force will ta'e. ;otice that the

force in Figure 1 is made up of several lines traveling in a specific direction. It can be

concluded that the lines travel from the magnet)s north pole to its south. 2hese lines of

force are often called the magnetic flu*. If the bar magnet is now bent to form ahorseshoe magnet, the north and south pole are now across from each other. ;otice in

the horseshoe magnet how the lines of force are now straight, and that they travel from

the north pole to the south. It will be revealed how generators and motors use these

lines of force to generate electricity, as well as mechanical motion.

Magnetic Fields Around Conductors8hen a current flows through a conductor, a magnetic field surrounds the conductor. $s

current flow increases, so does the number of lines of force in the magnetic field 5Fig. @7


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2he right hand rule helps demonstrate the relationship between conductor current and

the direction of force. Brasp a wire conductor in the right hand, put your thumb on the

wire pointing upward, and wrap your four fingers around the wire. $s long as the thumb

is in the direction that current flows through the wire, the fingers curl around the wire in

the direction of the magnetic field. Figure ! demonstrates the right hand rule.

olarity of Coils Cutting Through Lines of Force

$ conductor can be twisted into a coil, which efficiently produces current when cutting

the lines of force in a magnetic field. 2he more turns in this coil, the stronger the

magnetic field. Furthermore, if the coil is wrapped around a piece of iron, the current

becomes even stronger.

8hen needing to discover which poles are which in a conductor, it is important to notice

which way the coils turn in order to apply the right hand rule. In addition, one should

always loo' at which side of the coil is attached to the positive terminal of a power

source such as a battery, and which side is attached to the negative. Figure C illustrates

four different scenarios and the appropriate poles.


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$s a conductor cuts across the lines of force in a magnetic field, it generates a current.

2his method of inducing a current is called induction. 2here are three rules for inductionA

1. 8hen a conductor cuts through lines of force, it induces an electromotive force5EMF7, or voltage.

@. Either the magnetic field or the conductor needs to be moving for this to happen.

!. If the direction of the cutting across the magnetic field changes, the direction ofthe induced EMF also changes.

$ccordingly, Faraday)s law states that induced voltage can be determined by the

number of turns in a coil, and how fast the coil cuts through a magnetic field. 2herefore,

the more turns in a coil or the stronger the magnetic field, the more voltage induced.

In addition, current changes direction depending on which way it cuts across a magnetic

field. $s depicted in Figure ?, a coil cutting through a basic magnetic field in a cloc'wise

direction will at first result in a current with positive polarity, but as it cuts across the

same field in the opposite direction during the second half of its turn, the polarity

becomes negative.


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8hen current switches from positive to negative repeatedly, it is called alternating

current, or $.. $lternating current will be e*plained in more detail later.

!C Current

8hen a current is direct 5..7 rather than alternating 5$..7, the polarity of that current

never changes direction. -sually, when a coil turns in a cloc'wise direction, the first 1"

degrees of the turn result in the induced current going in a positive direction. $s

mentioned above, however, the second 1" degrees result in the induced current going

in a negative direction. In direct current, the current always travels in a positive

direction. &ow is this possibleD 8hen inducing direct current, some mechanism must be

employed to ma'e sure the coils only cut through the magnetic field in one direction, or

that the circuit only uses current from the coil cutting in that one direction. evices such

as .. generators employ a mechanism called a commutator to 'eep current flowing in

one direction. Figure shows direct current in the form of a sine wave. ;otice that the

current never has negative polarity, and is therefore always flowing in a positive

direction.


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!irect Current "enerators

$ generator is a device that turns rotary mechanical energy into electrical energy.

/imple .. generators contain several parts, including an armature 5or rotor7, a

commutator, brushes, and field winding. $ variety of sources can supply mechanicalenergy to the .. generator to turn its armature. 2he commutator changes the

alternating current 5$..7 into direct current as it flows through the armature.

2he stationary brushes, which are graphite connectors on the generator, form contact

with opposite parts of the commutator. $s the armature coil turns, it cuts across the

magnetic field, and current is induced. $t the first half turn of the armature coil

5cloc'wise direction7, the contacts between commutator and brushes are reversed, or to

put it another way, the first brush now contacts the opposite segment that it was

touching during the first half turn while the second brush contacts the segment opposite

the one it touched on the first half turn. (y doing this, the brushes 'eep current going inone direction, and deliver it to and from its destination.

!irect Current Motors

Motors change electric energy into mechanical energy. irect current motors and

generators are constructed very similarly. 2hey function almost oppositely at first

because a generator creates voltage when conductors cut across the lines of force in a

magnetic field, while motors result in tor+ue a turning effort of mechanical rotation.

/imple motors have a flat coil that carries current that rotates in a magnetic field. 2he

motor acts as a generator since after starting, it produces an opposing current byrotating in a magnetic field, which in turn results in physical motion.


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2his is accomplished as a conductor is passed through a magnetic field, then the

opposing fields repel each other to cause physical motion. 2he left hand rule can beused to e*plain the way a simple motor wor's 5Figure 7. 2he pointer finger points in the

direction of the magnetic field, the middle finger points in the direction of the current,

and the thumb shows which way the conductor will be forced to move.

$ selfe*cited motor produces its own field e*citation. $ shunt motor has its field in

parallel with the armature circuit, and a series motor is when the field is in a series with

the armature.

8hen the conductor is bent into a coil, the physical motion performs an up and down

cycle. 2he more bends in a coil, the less pulsating the movement will be. 2his physical

movement is called tor+ue, and can be measured in the e+uationA

T # $t ia


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T> tor+ue

$t> constant depending on physical dimension of motor

%> total number of lines of flu* entering the armature from one ; pole

ia> armature currentAlternating Current

Much li'e the process of producing direct current, the process of producing an

alternating current re+uires a conductor loop spinning in a magnetic field. $s a matter of

fact, the process is the same for both types of current, e*cept that the alternating

current is never changed into direct current through the use of a commutator. 2he

conductor loop, or coil, cuts through lines of force in a magnetic field to induce $..

voltage at its terminals. Each complete turn of the loop is called a Gcycle.G 2he

alternating current wave is pictured in Figure 1".

;otice what segment of the wave consists of one cycle, and which is the part of the

wave from point $ to the ne*t point $. If we divide the wave into four e+ual parts, the

divisions happen at points $, (, , and . 8e can read the turn of the coil and how it

relates to the wave produced. From $ to ( is the first +uarter turn of the coil, from ( to

is the second +uarter turn, from to is the third +uarter turn, and from to $ is the

final +uarter turn.

It is important to note that degree mar'ings on a hori3ontal a*is refer to electrical

degrees and are not geometric. 2he e*ample above is for a single pole generator.

&owever, if this were a double pole generator, then 1 cycle would happen at each 1"

degrees rather than !" degrees, and so on.

Alternating Current "enerator

$n alternating current generator, or alternator, produces an alternating current, which

means the polarity of the current changes direction repeatedly. 2his type of generator

re+uires a coil to cut across a magnetic field, and is attached to two slip rings connected


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to brushes. 2he brushes deliver the current to and from the load destination, thus

completing the circuit.

uring the first half turn, the coil cuts across the field near the magnet)s north pole.

Electrons go up the wire, and the lower slip ring becomes positively charged. 8hen the

coil cuts near the south pole of the wire during the second half turn, the lower slip ringbecomes negatively charged, and electrons move down the wire. 2he faster the coil

turns, the faster the electrons move, or to put it another way, the more fre+uency is

increased, or the more hert3 per second, the stronger the current.

Alternating Current Motor

$n alternating current motor is similar to the direct current motor e*cept for a few

characteristics. Instead of the rotor field reversing every half turn, the stator field

reverses every half turn.

2here are several different types of alternating current motors. 2he most common type

is the polyphase induction motor, which contain a stator and a rotor, where the stator is

attached to the $.. supply. 8hen the stator winding becomes energi3ed, a rotating

magnetic field is created. $n EMF is induced as the field goes across the inductors and


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current flows through them. 2or+ue is therefore e*erted on the rotor conductors carrying

current in the stator.

Faraday's Law of Electromagnetic Induction.docx

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