Title: ELECTROMAGNETIC INDUCTION
1UNIT 20 ELECTROMAGNETIC INDUCTION
Electromagnetic induction is the production of
an electrical potential difference (induced
emf) across a conductor situated in a changing
magnetic field.
20.1 Magnetic flux 20.2 Induced emf 20.3
Selfinductance 20.4 Mutual inductance 20.5
Energy stored in inductor
220.1 MAGNETIC FLUX ,F
 is defined as the scalar product between
 the magnetic flux density, B and the vector
 of the surface area, A.
UnitT.m2 or Wb
? 90?
? 0?
3Example 20.1.1
 A small surface of area 10 mm2 inside a uniform
magnetic field of strength 0.10 T is inclined at
an angle a to the direction of the field.
Determine the magnetic flux through the surface
if  a 0º,
 a 30º
 a 90º
Solution
420.2 INDUCED EMF
 An electric current produces a magnetic field.
 (chapter 19)
If electric currents produce a magnetic field, is
it possible that a magnetic field can produce an
electric current ?
 Scientists (American Joseph Henry and the
 Englishman Michael Faraday) independently
 found that is possible.
 Henry actually made the discovery first, but
 Faraday published his results earlier and
 investigated the subject in more detail.
520.2 INDUCED EMF
 The diagram below shows the apparatus used
 by Faraday in his attempt to produce an
 electric current from a magnetic field.
Faradays experiment to induce an emf
620.2 INDUCED EMF
 In this experiment, Faraday hoped by using a
 strong enough battery, a steady current in X
 would produce a current in a second coil Y but
 failed.
 Faraday saw the galvanometer in circuit Y
 deflect strongly at the moment he closed the
 switch in circuit X.
 And the galvanometer deflected strongly in
 the opposite direction when he opened the
 switch.
 A steady current in X had produced no
 current in Y.
720.2 INDUCED EMF
 Only when the current in X was starting or
 stopping was a current produced in Y.
 Faraday concluded that although a steady
 magnetic field produces no current, a
 changing magnetic field can produce an
 electric current.
 Such a current is called an induced current.
 We therefore say that an induced current is
 produced by a changing magnetic field.
 The corresponding emf required to cause
 this current is called an induced emf.
820.2 INDUCED EMF
 Induced emf is an electromotive force
 resulting from the motion of a conductor
 through a magnetic field , or from a change in
 the magnetic flux that threads a conductor.
 Faraday did further experiments on
electromagnetic induction, as this phenomenon is
called.( refer diagram )
 A current is induced when a magnet is
 moved toward a coil/loop.
b) The induced current is opposite when the
magnet is moved away from the coil/loop.
c) No current is induced if the magnet does
not move relative to the coil/loop.
9(No Transcript)
1020.2 INDUCED EMF
Micheal Faradays experiment
1120.2 INDUCED EMF
Micheal Faradays experiment
1220.2 INDUCED EMF
 Direction of the induced current depends on
 i ) the direction of the magnets motion and
 ii) the direction of the magnetic field.
 Magnitude of the induced current depends on
 i ) the speed of motion (v ?,Iind?)
 ii) the number of turns of the coil (N ?, Iind?)
 iii)the strength of the magnetic field (B?,Iind?)
 From the observations, Michael Faraday
 found that,
the current/emf is induced in a coil/loop or
complete circuit whenever there is a change in
the magnetic flux through the area surrounded by
the coil
1320.2 INDUCED EMF
Faradays law and Lenzs law
Faradays law
the magnitude of the induced e.m.f. is
proportional to the rate of change of the
magnetic flux
Lenzs law
an induced electric current always flows in such
a direction that it opposes the change producing
it.
1420.2 INDUCED EMF
Faradays law and Lenzs law
 These two laws are summed up in the
 relationship,
or
The () sign indicates that the direction of
induced e.m.f. always opposes the change of
magnetic flux producing it (Lenzs law).
1520.2 INDUCED EMF
Faradays law and Lenzs law
 The concept of Faraday's Law is that any change
 in the magnetic environment of a coil of wire
will  cause a voltage (emf) to be "induced" in the
coil.  No matter how the change is produced, the
 voltage will be generated.
 The change could be produced by
 a) changing the magnetic field strength,
 b) moving a magnet toward or away from the
 coil,
 c) moving the coil into or out of the magnetic
 field,
 d) rotating the coil relative to the magnet,
etc.
16(A) Induced emf in coil
20.2 INDUCED EMF
Faradays law and Lenzs law
17(A) Induced emf in coil
20.2 INDUCED EMF
Faradays law and Lenzs law
Notes
i ) the magnitude of induced emf,
ii) the flux through the coil can change in any
of 3 ways,
a) B , b) A , c) ?
18(A) Induced emf in coil
20.2 INDUCED EMF
Faradays law and Lenzs law
Notes
iii)
If the coil is connected in series to a resistor
of resistance R and the induced e.m.f ? exist in
the coil as shown in figure below.
and

19 Lenz's Law (based on censervation of energy)
 When an emf is generated by a change in magnetic
flux according to Faraday's Law, the polarity of
the induced emf (next slide) is such that it
produces a current whose magnetic field opposes
the change which produces it.  The induced magnetic field inside any loop of
wire always acts to keep the magnetic flux in the
loop constant.  In the examples below, if the B field is
increasing, the induced field acts in opposition
to it.  If it is decreasing, the induced field acts in
the direction of the applied field to try to keep
it constant.
20(A) Induced emf in coil
7.2 INDUCED EMF
Faradays law and Lenzs law
The polarity of the induced emf Induced current
is directed out of the positive terminal, through
the attached device (resistance) and into the
negative terminal.
21(A) Induced emf in coil
Faradays law and Lenzs law
Example 20.2.1
A coil of wire 8 cm in diameter has 50 turns and
is placed in a B field of 1.8 T. If the B field
is reduced to 0.6 T in 0.002 s , calculate the
induced emf.
22Solution
Faradays law and Lenzs law
d 8 cm, N 50 turns, B from 1.8 T to 0.6 T in
0.002 s
23(A) Induced emf in coil
Faradays law and Lenzs law
Example 20.2.2
An elastic circular loop in the plane of the
paper lies in a 0.75 T magnetic field pointing
into the paper. If the loops diamater changes
from 20.0 cm to 6.0 cm in 0.50 s,
 What is the direction of the induced current,
 What is the magnitude of the average induced emf,
and  If the loops resistance is 2.5 O, what is the
average induced current during the 0.50 s ?
24Faradays law and Lenzs law
Solution
B0.75 T, di 20.0 cm, df 6.0 cm, t 0.50 s
 Direction of the induced current,

 b) Magnitude of the average induced emf,
c) R 2.5 O,
25Example 20.2.3
Faradays law and Lenzs law
A circular shaped coil 3.05 cm in radius,
containing 40 turns and have a resistance of
3.55 ? is placed perpendicular to a magnetic
field of flux density of 1.25 x 102 T. If the
magnetic flux density is increased to 0.450 T in
time of 0.250 s, calculate the induced current
flows in the coil.
26(A) Induced emf in coil
Faradays law and Lenzs law
How to determine the direction of induced
current. Lenzs law
Case A
Thumb induced magnetic field Fingers  induced
current
N
Direction of induced current inducedcurrent
right hand rule.
27Faradays law and Lenzs law
How to determine the direction of induced
current. Lenzs law
Case A
 Consider a bar magnet that is moved
 towards a solenoid.
 As the north pole of the magnet approaches
 the solenoid, the amount of magnetic field
 passing through the solenoid increases ,
 thus increasing the magnetic flux through
 the solenoid.
 The increasing flux induces an emf
 (current) in the solenoid and galvanometer
 indicates that a current is flowing.
28Faradays law and Lenzs law
How to determine the direction of induced
current. Lenzs law
Case A
 The direction of the induced current is
 such as to generate a magnetic field in the
 direction that opposes the change in the
 magnetic flux, so the direction of the
 induced field must be in the direction that
 make the solenoid right end becomes a
 north pole.
 This opposes the motion of the bar magnet
 and obey the Lenzs law.
29Faradays law and Lenzs law
How to determine the direction of induced
current. Lenzs law
Case B
 When the magnet is moved toward the stationary
 conducting loop, a current is induced in the
 direction shown.
(b) This induced current produces its own
magnetic field (Binduced) directed to the
left that counteracts the increasing
external flux.
Binduced
Bexternal
30Faradays law and Lenzs law
How to determine the direction of induced
current. Lenzs law
Case B
(c) When the magnet is moved away from the
stationary conducting loop, a current is induced
in the direction shown.
(d) This induced current produces a magnetic
field (Binduced) directed to the right and
so counteracts the decreasing external flux.
Binduced
Bexternal
31(A) Induced emf in coil
Faradays law and Lenzs law
Faradays law and Lenzs law
Example 20.2.4
Calculate the current through a 37 O resistor
connected to a single turn circular loop 10 cm in
diameter, assuming that the magnetic field
through the loop is increasing at a rate of 0.050
T/s. State the direction of the current.
32Faradays law and Lenzs law
Example 20.2.4
R 37 O , d 10 cm dB/dt 0.050 T/s.
I induced
S
N
I induced
Direction of Iinduced from b to a.
33(B) Induced emf of a straight conductor
 Consider a straight conductor of length l is
moved at a speed v to the right on a Ushaped
conductor in a uniform magnetic field B that
points out the paper.
 This conductor travels a distance dx vdt in a
time dt.
34(B) Induced emf of a straight conductor
 The area of the loop increases by an amount
 According to Faradays law, the e.m.f. is
induced in the conductor and its magnitude is
given by
35(B) Induced emf of a straight conductor
? angle between v and B 90 o
 This induced emf is called motional induced emf.
36(B) Induced emf of a straight conductor
 As the conductor is moved to the right (Fapplied
to the right) with speed v, the magnetic flux
through the loop increases.
 A current is induced in the loop.
 The induced current flows in the direction that
tends to oppose this change.
Fapplied
FB
 In order to oppose this change, the current
through the conductor must produce a magnetic
force (FBIL) directed to the left.
37(B)Induced emf of a straight conductor
Faradays law and Lenzs law
 The direction of the induced current due to
induced e.m.f. flows in the linear conductor can
be determine by using Flemings right hand rule
(based on lenzs law).
P
 The induced current flows from P to Q.
Fapplied
FB
Fapplied
Q
Thumb direction of Motion First finger
direction of Field Second finger direction of
Induced current or
Induced e.m.f.
Only for the straight conductor.
38Polarity
(B)Induced emf of a straight conductor
 When the conductor is moved to the right
(Fapplied to the right) with speed v, the
electrons in the rod move with the same speed.
 Therefore, each feels a force FBqv, which acts
upward in the figure.
 If the rod were not in contact with the Ushaped
conductor, electrons would collect at the upper
end of the rod, leaving the lower end positive.
There must thus be an induced emf.
39Induced emf of a straight conductor
Example 20.2.5
Suppose the length in figure above is 0.10 m, the
velocity z is 2.5 m/s, the total resistance of
the loop is 0.030 O and B is 0.60 T. Calculate
a) the induced emf b) the induced current
c) the force acting on the rod d) the power
dissipated in the loop
40Induced emf of a straight conductor
Example 20.2.6
A 0.2m length of wire moves at a constant
velocity of 4 m/s in a direction that is 40 o
with respect to a magnetic flux density of 0.5 T.
Calculate the induced emf.
41Induced emf of a straight conductor
Example 20.2.7
In figure above, a rod with length l 0.400 m
moves in a magnetic flux with magnitude B 1.20
T. The emf induced in the moving rod is 3.60 V.
 Calculate the speed of the rod.
 If the total resistance is 0.900 O,
 calculate the induced current.
 What force does the field exert on the
 rod as a result of this current?
7.50 m/s , 4.00 A , 1.92 N to the left
42Fig 31CO, p.967
43(C) Induced emf in a rotating coil
An ac generator / dynamo (transforms mechanical
energy into electric energy)
44(C) Induced emf in a rotating coil
An ac generator / dynamo (transforms mechanical
energy into electric energy)
45(C) Induced emf in a rotating coil
 Consider a coil of N turns each of area A and is
being rotated about a horizontal axis in its own
plane at right angle to a uniform magnetic field
of flux density B.
 As the coil rotates with the angular speed ?,
the orientation of the loop changes with time.
46(C) Induced emf in a rotating coil
 The emf induced in the loop is given by
Faradays law,
 The emf induced in the loop varies sinusoidally
in time.
47(C) Induced emf in a rotating coil
The alternating emf induced in the loop plotted
as a function of time.
48Example 20.2.8
Induced emf in a rotating coil
The armature of a simple ac generator consists of
100 turns of wire, each having an area of 0.2 m2
. The armature is turned with a frequency of 60
rev/s in a constant magnetic field of flux
density 103 T. Calculate the maximum emf
generated.
49Example 20.2.9
Induced emf in a rotating coil
 The drawing shows a plot of the output emf of
a generator as a function of time t. The coil of
this device has a crosssectional area per turn
of 0.020 m2 and contains 150 turns. Calculate  The frequency of the generator in hertz.
 The angular speed in rad/s
 The magnitude of the magnetic field.
2.4 Hz , 15 rad/s , 0.62 T
50Example 20.2.10
Induced emf in a rotating coil
An amarture in ac generator consists of 500
turns, each of area 60 cm2 . The amarture is
rotated at a frequency of 3600 rpm in a uniform 2
mT magnetic field. Calculate a) the frequency
of the alternating emf b) the maximum emf
generated c) the instantaneous emf at time when
the plane of the coil makes an angle of 60o
with the magnetic field ?
380 rad/s, 1.13 V, 2.26 V
5120.3 SELFINDUCTANCE
 Selfinduction is defined as the process of
producing an induced e.m.f. in the coil due to a
change of current flowing through the same coil.
 Consider a current is present in the circuit
above.
5220.3 SELFINDUCTANCE
 This current produces a magnet field in the coil
that causes a magnetic flux through the same
coil.
 This flux changes when the current changes.
 An emf is induced in this coil called a
selfinduced emf.
 This coil is said to have selfinductance
 (inductance).
 A coil that has inductance is called an
 inductor.
5320.3 SELFINDUCTANCE
 The symbol for an inductor is
 if aircored, and if it
has  a core of magnetic material.
 By Lenzs law, the induced current opposes
 the change that cause it.
 If the current is increasing, the direction of
 the induced field and emf are opposite to that
 of the current, to try to decrease the current.
 If the current is decreasing, the direction of
 the induced field and emf are in the same
 direction as the current, to try to increase
the  current.
5420.3 SELFINDUCTANCE
Iinduced
Iinduced
 A current in the coil produces a magnetic field
 directed to the left.
(b) If the current increases, the increasing
magnetic flux creates an induced emf having
the polarity shown by the dashed battery.
(c) The polarity of the induced emf reverses if
the current decreases.
5520.3 SELFINDUCTANCE
 The magnetic flux in a coil is proportional
 to the current
. (1)
. (2)
5620.3 SELFINDUCTANCE
Selfinductance, L is defined as the ratio of the
self induced e.m.f. to the rate of change of
current in the coil.
5720.3 SELFINDUCTANCE
(1) (2)
If the coil has N turns, hence
 scalar quantity  unit is henry (H).
5820.3 SELFINDUCTANCE
 The value of the selfinductance depends on
 the size and shape of the coil
 the number of turn (N)
 the permeability of the medium in the
 coil (?).
 Selfinductance does not depend on current.
5920.3 SELFINDUCTANCE
Selfinductance of a Loop and Solenoid
From
And
By substituting we get,
or
For the mediumcore solenoid
or
where
6020.3 SELFINDUCTANCE
Example 20.3.1
If the current in a 230 mH coil changes steadily
from 20.0 mA to 28.0 mA in 140 ms, what is the
induced emf ?
Example 20.3.2
(Given ?0 4? x 107 H m1)
Suppose you wish to make a solenoid whose
selfinductance is 1.4 mH. The inductor is to
have a crosssectional area of 1.2 x 10 3 m2 and
a length of 0.052 m. How many turns of wire
needed ?
220 turns
6120.3 SELFINDUCTANCE
Example 20.3.3
The current in a coil of wire is initially zero
but increases at a constant rate after 10.0 s it
is 50.0 A. The changing current induces an emf of
45.0 V in the coil.
a) Calculate the self inductance of the coil.
b) Calculate the total magnetic flux through
the coil when the current is 50.0 A.
a)
b)
6220.3 SELFINDUCTANCE
Example 20.3.4
A 40.0 mA current is carried by a uniformly wound
aircore solenoid with 450 turns, a 15.0 mm
diameter and 12.0 cm length. Calculate a) the
magnetic field inside the solenoid. b) the
magnetic flux through each turn. c) the
inductance of the solenoid.
(Given ?0 4? x 107 H m1)
a)
b)
c)
or
6320.4 MUTUAL INDUCTANCE
20.4 MUTUAL INDUCTANCE
Mutual Inductance for two coaxial solenoids
 Consider a long solenoid with length l and cross
sectional area A is closely wound with N1 turns
of wire. A second solenoid with N2 turns
surrounds it at its centre as shown in figure
above.
6420.4 MUTUAL INDUCTANCE
Mutual Inductance for two coaxial solenoids
 The first solenoid is the one connected to an ac
 generator, which sends an alternating current
I1  through it.
 The current I1 produces a magnetic field lines
 inside it and this field lines also pass
through the  solenoid 2 as shown in figure.
 If the current I1 changes with time, the
magnetic  flux through the solenoids 1 and 2 will change
with  time simultaneously.
 Due to the change of magnetic flux through the
 solenoid 2, an e.m.f. is induced in solenoid 2.
 This process is known as mutual induction.
 At the same time, the selfinduction occurs in
the  solenoid 1 since the magnetic flux through it
changes.
65Mutual Inductance for two coaxial solenoids
20.4 MUTUAL INDUCTANCE
 Mutual induction is defined as the process of
producing an induced e.m.f.in one circuit/coil
due to the change of current in another
circuit/coil.
Mutual inductance, M
 If the current I1 in solenoid 1 is continously
changing,  then the flux it produces will also change
continously.
 The changing magnetic flux from the solenoid 1
 induces an emf in the solenoid 2.
 The induced emf in the solenoid 2 is
proportional to  the rate of change of the current I1 in
solenoid 1.
.. (1)
6620.4 MUTUAL INDUCTANCE
Mutual Inductance for two coaxial solenoids
Mutual inductance, M
 Also the induced emf in the solenoid 1 is
proportional  to the rate of change of the current I2 in
solenoid 2.
 The mutual inductance of the two solenoids is
the  same if current flows in the solenoid 2 and
flux links  the solenoid 1, causing an induced emf when a
 change in flux linkage occurs.
6720.4 MUTUAL INDUCTANCE
Mutual Inductance for two coaxial solenoids
Mutual inductance, M
M is defined as the ratio of the induced emf in
one solenoid/coil/ to the rate of change of
current in the other solenoid/coil.
.. (2)
68Mutual Inductance for two coaxial solenoids
20.4 MUTUAL INDUCTANCE
Mutual inductance, M
(1) (2)
 Since M12M21M, equation above can be
 written as
69Mutual Inductance for two coaxial solenoids
20.4 MUTUAL INDUCTANCE
Mutual inductance, M
and
 He mutual inductance of the solenoid 2 is,
7020.4 MUTUAL INDUCTANCE
Mutual inductance, M
7120.4 MUTUAL INDUCTANCE
Example 20.5.1
 The primary coil of a solenoid of radius 2.0 cm
has 500 turns and length of 24 cm. If the
secondary coil with 80 turns surrounds the
primary coil at its centre, calculate  a. the mutual inductance of the coils
 b. the magnitude of induced e.m.f. in secondary
coil if the current in primary coil changes at
the rate 4.8 A s1.
727.5 MUTUAL INDUCTANCE
Solution 20.5.1
rp 2.0 cm , Np 500 , lp 24 cm Ns 80
dIs/dt 4.8 A s1
a)
b)
73(No Transcript)
7420.4 MUTUAL INDUCTANCE
Transformer
 A transformer is a device for increasing or
 decreasing an ac voltage.
 The operation of transformer is based on the
 principle of mutual induction and
selfinduction.
7520.4 MUTUAL INDUCTANCE
Transformer
 Two types of transformer
 a) stepup transformer (Ns gt Np)
 b) stepdown transformer (Np gt Ns).
 There are three assential parts
 (1) a primary coil connected to an ac
source  (2) secondary coil
 (3) soft iron core
 When ac voltage is applied to the input coil
 (primary coil), the alternating current
produces  an alternating magnetic flux that is
concentrated  in the iron core, without any leakage of flux
 outside the core.
7620.5 ENERGY STORED IN INDUCTOR
 The functions of an inductor are
 to control current
 to keep energy in the form of magnetic field
 An inductor carrying current has energy
 stored in it.
 It is because a generator does work to
 establish a current in an inductor.
 Suppose an inductor is connected to a
 generator whose terminal voltage can be
 varied continously from zero to some final
 value.
7720.5 ENERGY STORED IN INDUCTOR
 As the voltage is increased, the current I in
the  circuit rises continously from zero to its
final value.  While the current is rising, an emf (back
 emf) is induced in the inductor.
 Because of this, the generator that supplies
the  current must maintain a potential difference
 between its terminals while the current is
rising  (changing), and therefore it must supply
energy to  the inductor.
 Thus, the generator must do work to push the
 charges through the inductor against this
induced  emf.
7820.5 ENERGY STORED IN INDUCTOR
 To do this, power has to be supplied by the
 generator to the inductor.
 The total work done while the current is
changed  from zero to its final value is given by
 This work is stored as energy in the inductor.
7920.5 ENERGY STORED IN INDUCTOR
 For a long aircore solenoid, the selfinductance
is
 Therefore the energy stored in the solenoid is
given by
Example 20.5.1
How much energy is stored in a 0.085H inductor
that carries a current of 2.5 A ?
8020.5 ENERGY STORED IN INDUCTOR
Example20.5.2
A steady current of 2.5 A in a coil of 500
turns causes a flux of 1.4 x 104 Wb to link
(pass through) the loops of the coil. Calculate
a) the average back emf induced in the coil if
the current is stopped in 0.08 s b) the
inductance of the coil and the energy
stored in the coil (inductor).