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Electromagnetic Induction
At first squint you might be
misled by this title picture
...
This is a
model of a hydropower
station which explains the
working of turbine and a
generator encapsulated in a
PVC transparent casing
...

Think
about
“FlinStone” time when
there was no electricity and
life was difficult
...
Today all
generators,
transformers
and high performance
machines are working on
the
principles
of
electromagnetic induction
...
In this
chapter we will explore the
insight of electromagnetic
induction and realise its
significance
...
1 INTRODUCTION
Now gradually we are proceeding towards the application of electromagnetism which we
have studied earlier
...
g
...

In the same way if we introduce E
...
F, current or magnetic properties, it will be known
as induced E
...
F, induced current or induced magnetism respectively
...

Electromagnetic induction is the most common area of physics with which people
normally deal with; for example generators, transformers, electric bells, relays,
loudspeakers are their common examples
...


8
...

By definition “the product of magnetic flux density and perpendicular area is called
magnetic flux”
...
So 1W  1T  m 2

WEBER:
If a magnetic flux density of 1T passes normally an area of 1m 2 then magnetic flux is said
to be of 1 Weber
...


CASE # 1:

“  ”with the plane

So B sin  is the perpendicular component to area A
...
Therefore
  B cos  A
  BA cos 
So if   0 0 , cos 0 0  1 and  max  B  A
Similarly if   90 0 , cos 90 0  0 and min  0

8
...
1 FLUX LINKAGE
This is number of field lines passing through number of perpendicular areas
...
”
Flux linkage  N  
Flux linkage  NBA
Again the unit is Weber
...


CASE # 1: “  ”with the plane of area
...


Flux Linkage  B cos   A  N
Flux Linkage  NBA cos
So if   0 0 , cos 0 0  1 Flux linkage  NBA
If   90 0 , cos 90 0  0 Flux Linkage  0
In electromagnetic induction we are interested in understanding the properties of induced
magnetism, their patterns and finally what are the consequences and uses of this
induction
...


8
...

Micheal Faraday was the scientist who first explained nature of electromagnetic
induction and intelligently translated law of conservation of energy into law of
electromagnetic induction
...
M
...
”
What is this? How we can understand it…
...

Whenever there is change in magnetic flux there is production of induced E
...
F
...
Look
at the following figure carefully
...
If the wire is held from ends X and Y and moved perpendicular to the filed lines
then a deflection is seen on the voltmeter
...
Now when a wire passes perpendicularly, the free electrons are
pushed to either side with some energy by the field lines and energy per unit charge is
called E
...
F, hence an E
...
F is induced
...


In this way an E
...
F is generated because field lines produce a gap
...
M
...
If we continuously move the wire, there is production of continuous

E
...
F and hence the voltmeter pointer will deflect in both directions if wire is moved
vertically up and down continuously
...
M
...
Similarly
with high magnetic flux density, again the E
...
F is maximum
...
M
...
e
...

Mathematically
𝑑∅
∆∅
𝜀= −
=−
𝑑𝑡
∆𝑡
Where negative sign shows resistive nature of induced E
...
F, (We will discuss in detail
𝑑
about negative sign and why both directions? later)
...

Let’s start with some mathematical working and graphs
...


Then
𝜇 𝑜 𝐼𝑁
)
𝑙
𝜀= −
− − − − − − − − − (2)
𝑑𝑡
𝑑𝐼
so 𝜀 ∝ − 𝑑𝑡 − − − − − − − − − −(3)
Following graphs are helpful in understanding the relationship of current, magnetic flux
and current
...
Compare (1) and (3)
...

dt
But from (1) and (3) whatever is the case 𝜀 = −

Gradient is

𝑑∅
𝑑𝑡

, which shows that if gradient of  and

t is increasing, E
...
F is increasing and if it is decreasing  is decreasing and if zero it is
zero as well, so

Can you prove it mathematically? Yes look at the following working

d
dt
d BA 

dt
  IN  A
d 0

l



dt
dI
or  
dt
As we know that I  I 0 sin  t from the concept of A
...



d I 0 sin  t 
dt
d
or   I 0 sin  t
dt
d
as sin  t   cos  t
dt
so   I 0 cos  t
Do you this equation is for a negative cosine wave? If yes then tally with figure (3)
...

Suppose if a graph for magnetic flux density is like below
...

When gradient is minimum positive, E
...
F is minimum constant but negative
...
M
...

When in (3) it is greater than (2) then E
...
F is greater in negative and finally in (4) the
gradient is negative having maximum magnitude, therefore E
...
F is positive and having
maximum magnitude
...
Following law is useful to understand the situation
...
4 LENZ’S LAW
Lenz was the first scientist who investigated the direction of induced current
...
In other words suppose if one
million people produce an induced current with the similar experimental conditions and
circumstances then all of them will get the same direction of induced current
...

“The direction of induced current is such that to oppose the cause of change
(disturbance) in magnetic flux
...
If we read this law in conjunction with Faraday’s Law
of electromagnetic induction then this law will be clear
...

Whenever there is change in magnetic flux, there is production of induced E
...
F hence
current is produced such that its direction is to oppose the cause of disturbance
...
This is a very clear intuition
...
g
...
This current produces a new magnetic field around the
wire which combines with primary magnetic field and the resultant force opposes the
cause of disturbance (not disturbance)
...

8
...
1 SELF INDUCTION
Suppose a bar magnetic is inserted in the solenoid
...
Now if you are asked to avoid this disturbance or
stop this disturbance what will you do?

You are available with only two options, either move the bar magnet back towards right
or move the solenoid away toward left
...
It is observed that at this time like pole is created on the
facing side of solenoid, and this is due to the current which flows in such direction to
produce similar pole when magnet is inserted
...


CASE # 1:

Now you will understand that whenever there is change in magnetic flux, there is
production of induced E
...
F, hence current is produced such that the direction is to
oppose the cause of disturbance in magnetic flux
...
e
...

Current needs to flow in such a way that the cause is opposed so repulsion is observed
due to the production of like polarity
...
But if again bar
is moved out of magnet again there will be disturbance and hence again current is
produced to oppose the cause so flows in opposite direction and opposite pole is
increased therefore attraction is felt as shown below
...

1
...


3
...


8
...
2 MUTUAL INDUCTION
Suppose there are two solenoids, one connected with a galvanometer and the other with a
battery (power supply) as shown in figure
...
When switch of
solenoid 2 is closed both solenoids repel each other because of disturbance in magnetic
field
...
When switch is
opened again magnetic flux is changed and both solenoids attract each other in order to
avoid disturbance
...

If you want to produce continuous current in solenoid 1, you need to either continuously
switch ON and OFF the current, or to provide an A
...

Now one question left, why negative sign is used with the mathematical expression of
Faraday’s Law of electromagnetic induction
d
 
dt
Recall Lenz’s Law, current has to oppose the cause of disturbance
...
M
...
M
...
M
...


8
...
According to this rule
“If finger of indication, middle finger and the thumb of the right hand are placed
perpendicular to each other; then; indication finger gives direction of magnetic field
lines, middle finger gives the direction of current and thumb gives the direction of
motion of wire
...


So if wire is moved downwards perpendicular to magnetic field lines then using right
hand rule current is towards X
...


8
...
6
...
C) MOTOR
Following figure gives a view of a D
...


A D
...
A set
of split ring commutators with carbon bushes are connected as shown in figure
...
Quarter revolution is made due to
magnetic field force and the other quarter due to momentum of armature
...

Following diagrams can give complete understanding to its working
...
Apply Fleming’s left
hand rule
...

  Fx
Where x  perpendicular distance between the forces  BD
In this position the current should be stooped in armature which is successfully done by
the commutators, which are not in contact with carbon bushes, hence current may not be
enter or leave the armature
...


Apply Fleming’s left hand rule to find the direction of magnetic field forces
...

Next 90 0 are covered due to momentum and there is no magnetic field force
...


Again contact of commutators and carbon bushes is established and again magnetic field
forces are introduced to produce torque
...

If you want to calculate magnetic flux density, you can easily calculate it using following
formula
...
e
...
, ' AB'
F
Then B   AB 
I  AB
Suppose if number of turns of armature is provided then
 F 
B
 N
 I  AB 
Where N  number of turns
This can be used to find total magnetic field force
...
CURRENT:
Speed  I
As with high current high magnitude couple is produced, resulting in high magnitude of
torque
...
MAGNETIC FIELD STRENGTH B :
Speed  B
With high magnetic flux density, there will be stronger magnetic field force and hence
high magnitude of torque is introduced
...
NO
...
of turns of armature
With greater no
...


1
...
C GENERATORS:
A
...
An A
...


Following diagram may help to understand the working of an A
...
Slip rings
allow two flow of current
...
How current reverses? We have to critically analyze the motion of armature
...
The wire section AB is into the page
...


When wire is at position (1), instantaneous velocity is parallel to field lines, hence no
current is introduced
...
From (3) to (5) it decreases and again zero when reaches at (5)
...

Following graph can be used to depict this situation
...


FACTORS AFFECTING PEAK VALUE I / N  :
1
...
C cycle both increase
...
Following graphs are helpful to understand
above text
...
MAGNETIC FLUX DENSITY B :
With more magnetic flux density B , there will be more disturbances hence more emf and
current is generated but frequency is unaltered
...
NO
...
of turns there is more disturbance, hence more voltage is produced
...
C motor is supplied with the fixed emf, initially speed of rotation of armature is
high but later it decreases
...
This introduces a resistance towards supplied EMF is consumed is
overcoming the back emf, therefore less voltage is received by armature as net voltage
responsible to rotate it about its centroidal axis
...
TRANSFORMER:
This is a device used to convert voltages
...
In this section we will emphasize on magnetic flux density and its changes
...

1
...

2
...

Quickly going through the knowledge already in hand
...
of turns in
secondary coil are responsible to change magnetic flux density, therefore more emf is
induced
...
of turns in primary coil
N s  No
...

d
 
dt
In order to provide continues magnetic flux density, an A
...
So a transformer can
only work with variable A
...
C output
...
STEP-UP TRANSFORMER:
These are used to convert low voltage into high voltage so,
Ns  N p

2
...
e
...
i
...
,
Po  Pi
as P  V  I
so Vs  I s  V p  I p
Vp

Is
Vs
Ip
Look at the relation carefully, you will identify that if voltage decrease current increases and vise
versa
...
Secondly remember that transformer is a non-ohmic device so
current decreases when voltage increases
...

Nature avoids disturbance
...
Therefore eddy current is produced
...
Now when disc
enters the field, there is change in magnetic flux, so an induced emf is generated at the entering
end so a current is produced
...
Hence a new magnetic field emerges around the disc combining with permanent
magnetic field
...


If you want to continue oscillations of same amplitude, you need to break flow of eddy current
...

Eddy current is the disturbance in the transformer if made from continues metal block as shown
below
...
This avoided by using laminated iron
core which stops circulation of eddy current
...


Eddy current may work as an advantage as well
...


An iron disc attached with wheels is placed between an electromagnet
...

The magnetic flux density changes hence causing an eddy current to be introduced in the disc
...




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