This document is a student project on electromagnetic induction submitted by Shubham Kourav to his teacher Mrs. Pratiksha Lawana. It includes an introduction to electromagnetic induction, a history of its discovery, experiments conducted by Faraday and Henry, applications of electromagnetic induction including generators and transformers, and concepts such as Lenz's law, eddy currents, and self and mutual induction. The project aims to study electromagnetic induction and contains sections on magnetic flux, Faraday's law, Maxwell's equations, and more.

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SESSION 2014-2015
INVESTIGATORYPROJECTON -
“Electromagnetic induction”
CLASS-12
SUBMITTED TO SUBMITTED BY
Mrs. PRATIKSHA LAWANA shubham kouraV

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CERTIFICATE
THIS IS TO CERTIFY THAT THE PROJECTENTITLED “ELECTROMAGNETIC INDUCTION” WHICH HAS
BEENCOMPLETEDAND SUBMITTEDBY “SHUBHAMKOURAV”STUDENTOFCLASS 12TH
M/S. YEAR
2014-2015 OFADITYA CONVENTSCHOOL,IS A BONAFIEDWORKOF HIM.
SUBMITTED BY
SHUBHAM KOURAV DATE: / /
ROLL NO.-
PRINCIPAL TEACHER
ACKNOWLEDGEMENT

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I ACKNOWLEDGE THE VALUABLE SUGGESTION AND ADVICE
BY Mrs. PRATIKSHA LAWANA (PHYSICS TEACHER), ADITYA
CONVENT SCHOOL, JABALPUR FOR ENCOURAGING ME FOR
THIS PROJECT. I TAKE THIS OPPORTUNITY TO EXPRESS MY
GRATITUDE FOR HIS GUIDANCE DURING THE COURSE OF
THIS PROJECT WORK.I AM ALSO GRATEFUL TO THE
RESPECTED PRINCIPAL Mrs. VINITA MAHESHWARI (PRICIPAL)
FOR HER KIND HELP AND COOPERATION EXTENDED FOR ME
DURING THE COURSE OF THE PROJECT.
I CAN’T FORGET TO OFFER MY SINCERE THANKS TO
PARENTS AND ALSO TO MY CLASSMATES WHO HELPED ME
TO CARRY OUT THIS PROJECT WORK SUCCESSFUL AND FOR
THEIR VALUABLE ADVICE AND SUPPORT, WHICH I RECEIVED
FROM THEM TIME TO TIME….
LIST OF CONTENTS:
CERTIFICATE
ACKNOWLEDGEMENT
AIM
INTRODUCTION
HISTORY
MAGNETIC FLUX
FARADAY’S EXPERIMENT
INDUCED E.M.F’S
FARADAY’S LAW AND THE MAXWELL FARADAY EQUATION

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MAXWELL-FARADAY EQUATION
APPLICATIONS
APPLICATIONS OF ELECTROMAGNETIC INDUCTION
LENZ’S LAW
LENZ’S LAW AND ENERGY CONSERVATION
RIGHT HAND THUMB RULE
EDDY’S CURRENTS OR FOUCAULT CURRENTS
APPLICATIONS OF EDDY CURRENTS
SELF INDUCTION
MUTUAL INDUCTION
MUTUAL INDUCTION OF TWO LONG COAXIAL SOLENOIDS
ADDITIONAL INFORMATION
CONCLUSION
BIBLIOGRAPHY
AIM:

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STUDY OF “ELECTROMAGNETIC
INDUCTION”

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ELECTRO MAGNET:
An electromagnet is a type of magnet in which the magnetic field is produced
by electric current. The magnetic field disappears when the current is turned off.
INDUCTION:
This process of generating current in a conductor by placing the conductor in a
changing magnetic field is called induction.
ELECTROMAGNETIC INDUCTION:
Electromagnetic induction is the production of an electromotive force across a
conductor when it is exposed to a varying magnetic field. It is described
mathematically by Faraday's law of induction. Faraday's law of induction is a basic
law of electromagnetism predicting how a magnetic field will interact with an
electric circuit to produce an electromotive force (EMF).
It is the fundamental operating principle of transformers, inductors, and many
typesof electrical motors, generators and solenoids. Electricity is carried by current,
or the flow of electrons. One useful characteristic of current is that it creates its own
magnetic field. This is useful in many types of motors and appliances.
Electromagnetic induction is the production of a potential difference (voltage)
across a conductor when it is exposed to a varying magnetic field.

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Electromagnetic induction is when an electromagnetic field causes molecules in
another object to flow. Induction can produce electricity (in coils), heat (in ferrous
metals), or waves (in a radio transmitter).Finally it is refers to the phenomenon
where an emf is induced when the magnetic flux linking a conductor changes.
HISTORY:
Electromagnetic induction was discovered independently by MichaelFaraday in
1831 and JosephHenry in 1832. Also, Faraday wasthe first to publish the resultsof
his experiments. In Faraday'sfirst experimentaldemonstration (August29, 1831),
he wrapped two wiresaround oppositesidesof an iron ring or "torus" (an
arrangementsimilar to a modern toroidaltransformer). Based on his assessment of
recently discovered propertiesof electromagnets, he expected that when current
started to flow in one wire, a sort of wave would travelthrough the ringand cause
some electrical effect on the opposite side. He plugged onewireinto a galvanometer,
and watched it as he connected the other wire to a battery. Indeed, he saw a
transient current(which he called a "wave of electricity") when he connected the
wire to the battery, and another when he disconnected it. This induction wasdueto
the change in magnetic flux that occurred when the battery was connected and
disconnected. Within two months, Faraday found severalother manifestationsof
electromagnetic induction. For example, he saw transient currentswhen he quickly
slid a bar magnet in and outof a coil of wires, and he generated a steady (DC)
currentby rotating a copper disk near the bar magnet with a slidingelectrical lead
("Faraday'sdisk").
Faraday explained electromagnetic induction usinga concepthe called lines of force.
However, scientists at the time widely rejected his theoretical ideas, mainly because
they were not formulated mathematically. An exception was Maxwell, who used
Faraday'sideasas the basis of his quantitative electromagnetic theory. In Maxwell's
model, the time varyingaspect of electromagnetic induction is expressed as a
differentialequation which Oliver Heaviside referred to as Faraday'slaw even
though it is slightly differentfrom Faraday'soriginalformulation and doesnot
describe motional EMF. Heaviside'sversion (see Maxwell–Faraday equation)isthe
form recognized today in the group of equations known as Maxwell'sequations.

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Heinrich Lenz formulated the law named after him in 1834, to describethe "flux
through the circuit". Lenz'slaw gives the direction of the induced EMFand current
resulting from electromagnetic induction (elaborated upon in the examplesbelow).
Followingthe understandingbroughtby these laws, many kindsof device
employingmagnetic induction havebeen invented.
MAGNETIC FLUX (Φ or ΦB):
Magnetic Flux through any surfaceis the number of magnetic lines of force passing
normally through that surface.
It can also be defined as the magnetic flux (often denoted Φ or ΦB)through a surface
is the surfaceintegral of the normalcomponentof the magnetic field B passing
through that surface. Magneticflux is usually measured witha fluxmeter, which
contains measuringcoils and electronics that evaluatesthe change of voltage in the
measuringcoils to calculate the magnetic flux
Φ = B . A COSθ
* SI unitof magnetic fluxis Weber (in derived units: volt-seconds)or tesla-metre2
or (wb or Tm2).

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* CGSunit of magnetic fluxis Maxwell.
* 1 Maxwell= 10-8 Weber
Positive Flux:
Magnetic Flux is positivefor 0° ≤ θ < 90° & 270° < θ ≤ 360°
Zero Flux:
Magnetic Flux is zero for θ = 90° & θ = 270°
Negative Flux:
Magnetic Flux is negative for 90° < θ < 270°
Flux is maximum when θ = 0° and is Φ = B. A
Magnetic Flux across a coil can be changed by changing:
1) The strength of the magnetic field B
2) The area of cross section of the coil A
3) The orientation of the coil with magnetic field θ or
FARADAY’S EXPERIMENT:
 Faraday in 1831 firstdiscovered that whenever the number it of magnetic lines of
forces in a circuit changes, a e.m.f. is produced in the circuit and is known asinduced
e.m.f. and this phenomenon isknown asElectro Magnetic Induction.

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 If the circuit is closed one then a currentflowsthrough it which is known an induced
current.
 This induced e.m.f and currentlasts only for the time while magnetic flux is
changing.
 Wenow illustrate two examplesof the sort that faraday and Henry performed.
EXPERIMENT -1
 Figure below showsa closed circuit containingcoil of insulated wire.
 Also note that circuit does notcontain any source of emf so there is no deflection in
the galvanometer.
 If we movebar magnet towardsthe coil keepingthe coil stationary with north pole
of the magnetfacing the coil (say) then we notice deflection in needleof the
galvanometer indicating the presenceof the currentin the circuit
 This deflection observed is only for the time intervalduringwhich the magnet is in
motion
 Now if we begin to move the magnet in the oppositedirection then the
galvanometer needleis now deflected in the oppositedirection
 again if we movethe magnet towardsthe coil ,with its south polefacing the coil, the
deflection is now in opposite direction, again indicating that the currentnow setup
in the coil is in reversedirection to that when the north polefaces the wire
 A deflection is also observed in galvanometer when the magnet is held stationary
and circuit is moved away from the magnet.

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 It is further observed that faster is the motion of magnet, larger is the deflection in
the galvanometer needle.
 From this experimentfaraday convinced that magnetmovingtowardsthe coil one
way has the sameeffect movingcoil towardsthe magnet the other way.
EXPERIMENT -2
 Figure-2 given below showsa primary coilP connected to the battery and a
secondary coil connected to the galvanometer.
 Now we have replaced magnet of the previousexperimentwitha currentcarrying
coil and expect to observe similar effect as currentcarryingcoil producesmagnetic
field.
 The motion of either of the coils showsdeflection in the galvanometer.
 Also galvanometer shows a sudden deflection in one direction when currentwas
started in primary coil and in the oppositedirection when the currentwas stopped.
INDUCED E.M.F’S
An e.m.f. is induced in a coil, when amountof magnetic fluxlinked with the coil
changes with time .If magnetic fluxthrough a coil is altered then an e.m.f. will be
generated in the coil. This effect was first observed and explained by Ampereand

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Faraday between 1825 and 1831. Faraday discoveredthatan e.m.f. could be
generated either by,
(a) movingthe coil or the source of flux relative to each other or by
(b) changing the magnitudeof the sourceof magnetic flux in some way.
Note that the e.m.f. is only produced whilethe fluxis changing.
FARADAY’S LAW AND THE MAXWELL-FARADAY
EQUATION:
I Law:
Whenever the amount of magnetic flux linked with a circuit changes, an e.m.f. is induced in the
circuit. The induced e.m.f. lasts so long as the change in magnetic flux continues.
II Law:
The magnitude of the induced e.m.f. is directly proportional to the rate of change of magnetic
flux linked with a circuit.
E α dΦ / dt
E = k dΦ / dt
(Where k is a constant and unitsare chosen such that k = 1)
E = dΦ / dt
E = (Φ2 – Φ1) / t
If dΦ is small change in magnetic flux in a small time dt, weget
,
 Negative sign is taken because induced e.m.f. always opposes any changes in
magnetic flux associated with the circuit.
 Where is the electromotive force (E.M.F.)and ΦB is is the magnetic flux. The
direction of the electromotive force is given by Lenz’s law. This version of Faraday's
law strictly holds only when the closed circuit is a loop of infinitely thin wire, and is
invalid in someother circumstances. A differentversion, the Maxwell–Faraday
equation (discussed below), is valid in all circumstances.

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 For a tightly wound coilof wire, composed of N identical turns, each with the same
magnetic fluxgoing through them, the resultingEMFis given by
MAXWELL-FARADAY EQUATION:
The Maxwell–Faraday equation isa generalisation of Faraday'slaw that states that a
time-varyingmagnetic field is alwaysaccompanied by a spatially-varying, non-
conservative electric field, and vice-versa. The Maxwell–Faraday equation is
(In SI units) where is the curl operator and again E(r, t) is the electric
field and B(r, t) is the magnetic field. These fieldscan generally be functionsof
position r and time t.
The principles of electromagnetic induction are applied in many devices and
systems, including:

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 Current clamp
 Electrical generators
 Electromagnetic forming
 Graphics tablet
 Hall effect meters
 Induction cookers
 Induction motors
 Induction sealing
 Induction welding
 Inductive charging
 Inductors
 Magnetic flow meters
 Mechanically powered flashlight
 Pickups
 Rowland ring
 Transcranial magnetic stimulation
 Transformers
 Wireless energy transfer
APPLICATIONS OF ELECTROMAGNETIC INDUCTION:
ELECTRICAL GENERATOR:
The EMF generated by Faraday's law of induction due to relative movement of a circuit
and a magnetic field is the phenomenon underlying electrical generators. Electric

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generator moves a conductor in a magnetic field to produce voltage via electromagnetic
induction. When a permanent magnet is moved relative to a conductor, or vice versa, an
electromotive force is created. If the wire is connected through an electrical load, current
will flow, and thus electrical energy is generated, converting the mechanical energy of
motion to electrical energy.
ELECTRICAL TRANSFORMER:
The EMF predicted by Faraday's law is also responsible for electrical transformers. When
the electric current in a loop of wire changes, the changing current creates a changing
magnetic field. A second wire in reach of this magnetic field will experience this change in
magnetic field as a change in its coupled magnetic flux, d ΦB / d t. Therefore, an
electromotive force is set up in the second loop called the induced EMF or transformer
EMF. If the two ends of this loop are connected through an electrical load, current will
flow.
MAGNETIC FLOW METER:
Faraday'slaw is used for measuringthe flow of electrically conductiveliquidsand
slurries. Such instrumentsare called magnetic flow meters. The induced voltage ℇ

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generated in the magnetic field B dueto a conductiveliquid movingat velocity v is
thus given by:
where ℓ is the distance between electrodes in the magnetic flow meter.
LENZ’S LAW:
“The direction of the induced e.m.f. or induced current is such that it opposes the
change that is producing it”.
i.e. If the current is induced due to motion of the magnet, then the induced current
in the coil sets itself to stop the motion of the magnet.
If the current is induced due to change in current in the primary coil, then induced
current is such that it tends to stop the change.

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LENZ’S LAW AND ENERGY CONSERVATION:
Accordingto Lenz’s law, the induced emf opposesthe change that producesit. It is this
opposition against which we perform mechanicalwork in causing the change in
magnetic flux. “Therefore, mechanical energy is converted into electrical energy. Thus,
Lenz’slaw is in accordance with the law of conservation of energy”.
RIGHT HAND THUMB RULE:
This rulestates “If we stretch the central finger, forefinger and thumb of right hand
are stretched mutually perpendicular to each other and the forefinger pointsto
magnetic field, thumb pointsin the direction of motion (force), then central finger
pointsto the direction of induced currentin the conductor

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EDDY’S CURRENTS OR FOUCAULT CURRENTS:
“Eddy Currents arethe currents induced in the bulk pieces of conductorswhen the
amountof magnetic fluxlinked with the conductor changes”. However, their flow
patterns resembles swirlingeddiesin water. That is why they are called eddy currents.
There was discovered by Foucault in the year 1895 and hencethey are also called
Foucaultcurrents.
Conductors(of finite dimensions)movingthrougha uniform magneticfield, or
stationary within a changing magnetic field, will have currentsinduced within them.
These induced eddy currentscan be undesirable, sincethey dissipate energy in the
resistance of the conductor. There are a number of methods employed to control these
undesirableinductiveeffects.
APPLICATIONS OF EDDY CURRENTS:
 In induction furnaceeddy currentsareused for melting iron ore, etc.
 In speedometer eddy currentsareused to measurethe instantaneousspeed of the
vehicle.
 In dead beat galvanometer eddy currentsareused to stop the dampingof the coil in a
shorter interval.
 In electric brakes of the train eddy currentsare produced to stop the rotation of the
axle of the wheel.
 In energy meters (watt – meter) eddy currentsareused to measurethe consumption
of electric energy.
 In diathermy eddy currentsareused for localised heating of tissues in human
bodies.
 In electro-magnetic dampingeddy currentsareused in dead beat galvanometers.
 Electric power meter in house, etc.
Eddy currents (I,red) induced in a conductivemetal
plate(C) as it moves to right under a magnet (N).The
magnetic field (B,green) is directed downthrough the plate.
From Lenz's law the increasing field at the leading edge of
the magnet (left) induces a counterclockwisecurrent,which
creates its own magnetic field (left bluearrow) directed up,
whichopposes the magnet's field, producing a retarding
force.Similarly, at the trailing edge of the magnet (right),a
clockwisecurrent and downwardcounterfield is created (rightbluearrow) also producing a retarding force.

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SELF INDUCTION:
“Self induction is the property of a coil by virtue of which, the coil opposes any
changes in the strength of current flowing through it by inducing an e.m.f. in itself”.
When a current is induced by a changing magnetic field, that current itself produces
its own magnetic field. This effect is called self-induction.
Consider a coil connected to a battery through a rheostat as shown in figure. The
currentthrough the coil producesamagnetic fluxwhich links with the coil itself. If
we vary the resistance in the circuit, the currentthrough the coil changes and the
magnetic fluxthrough the coil also change. This change in fluxindicates an e.m.f. in
the coil itself. Such an e.m.f. is called self-induced e.m.f. and the phenomenon iscalled
self induction.
COEFFICIENT OF SELF INDUCTION-
Consider a single conductingcircuit around whicha current is flowing. This current
generates a magnetic field which gives rise to a magnetic flux linking the circuit.
Weexpect the flux to be directly proportionalto the current , given the linear
natureof the lawsof magnetostatics, and the definition of magnetic flux. Thus, we can
write
Φ α LI
or Φ = LI
(Where L is the constant of proportionality and isknown asSelf Inductanceor co-
efficient of self induction)
 Thus, self inductanceis defined asthe magnetic flux linked with a coil when unit
currentflowsthrough it.
If I = 1, then L = Φ

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 Thus, self inductanceis defined asthe induced e.m.f. set up in the coil through which
the rate of change of currentis unity.
Also,
And
If dI/ DT= 1, then L= - E
 Self inductanceis said to be 1 Henry when unit rate of change of current(1 A / s)
inducese.m.f. of 1 volt in the coil.
S.I. unitof self-inductanceis Henry (H)
i.e., 1 Henry = 1 Volt / ampere/second.
SELF INDUCTION OF A LONG SOLENOID –
Consider a solenoid of length and cross-sectional area . Supposethat the
solenoid has turns. When a current flowsin the solenoid, a uniform axialfield
of magnitude
is generated in the core of the solenoid. The field-strength outside the core is negligible. The
magnetic flux linking a single turn of the solenoid is . Thus, the magnetic flux linking
all turns of the solenoid is
According to Eq., the self inductance of the solenoid is given by , which reduces to

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Note that is positive. Furthermore, is a geometric quantity depending only on
the dimensions of the solenoid, and the number of turns in the solenoid.
MUTUAL INDUCTION:
“Mutual induction is the property of two coils by virtue of which each opposes any
change in the strength of current flowing through the other by developing an
induced e.m.f.” It is the phenomenon in which a change of current in one coil causes
an induced e.m.f. in another coil placed near to the first coil. The coil in which
current is changed is called primary coil and the coil in which e.m.f. is induced is
called secondary coil.
Mutual Induction is the phenomenon of inducing e.m.f. in the secondary coil due to
change in current in the primary coil and hence the change in magnetic flux in the
secondary coil.
COEFFICIENT OF MUTUAL INDUCTION-
Φ21 α I1
or Φ21 = MI1
(Where M is the constant of proportionality and is known as Mutual Inductance or co-
efficient of mutual induction)
If I1 = 1, then M = Φ

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 Thus, mutualinductanceis defined asthe magnetic fluxlinked with the secondary coil
when unit current flows through the primary coil.
Also, E2 = - dΦ21 / dt
Or E 2= - M (dI1 / dt)
If dI1 / dt = 1, then M = - E
 Thus, mutual inductance is defined as the induced e.m.f. set up in the secondary coil
when the rate of change of current in primary coil is unity.
SI unit of mutual inductance is Henry (H).
 Mutual inductance is said to be 1 Henry, when a current changes at the rate of
(1 A / s) in primary coil induces e.m.f. of 1 volt in the secondary coil.
MUTUAL INDUCTION OF TWO LONG COAXIAL
SOLENOIDS:
Magnetic Field due to primary solenoid is
B1 = μ0n1I1
Magnetic Flux linked across one turn of the secondary solenoid is
Φ21 per turn = B1 A = μ0n1I1A = μ0N1I1A / l
Magnetic Flux linked across N turns of the secondary solenoid is
Φ21 = μ0N1N2I1A / l
But, Φ21 = M21I1

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M21 = μ0N1N2A / l = μ0n1n2Al
lllly M12 = μ0N1N2A / l = μ0n1n2Al
For two long co-axial solenoids of same length and cross-sectional area, the
mutual inductance is same and leads to principle of reciprocity.
M = M12 = M21
Uses of Electro Magnetic Induction:
 Electromagnetic induction includes, Generators, Transformers, ElectricCookers,
Detecting hidden detects.
 It produceselectricity.
ADDITIONAL INFORMATION:
1)If the two solenoids are wound on a magnetic core of relative permeability μr, then
M = μ0 μr N1N2A / l
2)If the solenoids S1 and S2 have no. of turns N1 and N2 of different radii r1 and r2
(r1 < r2), then
M = μ0 μr N1N2 (πr1
2)/ l
3)Mutual inductance depends also on the relative placement of the solenoids.
4)Co-efficient of Coupling (K) between two coils having self-inductance L1 and L2 and
mutual inductance M is
K = M / (√L1L2) Generally, K < 1
5)If L1 and L2 are in series, then L = L1 + L2.
6)If L1 and L2 are in parallel, then (1/L) = (1/L1) + (1/L2) .

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CONCLUSION
Electromagnetic induction is the production of an electromotive force that results from the
movement of a conductor through a magnetic field. An electromotive force also results from the
changing of magnetic flux in a closed loop circuit.
Magnetic fields and electric fields are both components of an electromagnetic wave. In such a wave,
the electrical and magnetic fields potentiate each other.
Within most electrical circuits, an electromotive force, or EMF is produced by a source of potential
difference within a circuit. The source of potential difference is usually some form of battery of
capacitor.
Electromotive force drives current flow between areas of differing voltages in a conducting
material. The movement of charges or current flow is directly proportional to the EMF and
inversely related to the resistance of the conducting material.
An EMF that causes current within a circuit can, hopwever, be created from an putside source as
wll. In its most usual form, electromagnetic induction refers to the induction of an electromagnetic
force within a conductor by an external magnetic field. A current that is produced in a circuit
without a battery or other source of electrical potential is called an induced current.
The electromagnetic induction of current by a magnetic field occurs only when the magnetic field is
changing. Shifting magitude or direction of a magnetic field is called magnetic flux change. A
current is induced within a conductor existing inside of a magnetic field when magnetic flux
changes with time. This principle, that the induced electromotive force through a circuit is equal to
the rate of change of magnetic flux through it, is known as Faraday's law of induction, first
demonstrated by Faraday.

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BIBLIOGRAPHY
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COMPREHENSIVE CHEMISTRY PRACTICAL CLASS 12TH