24 pius augustine em induction & ac

1
Electromagnetic Induction & AC

Electromagnetic Induction and AC
Dr. Pius Augustine, S H College, Kochi

A student asserted that if a
permanent magnet is dropped
down a vertical copper pipe, it
eventually reaches a terminal
velocity even if there is no air
resistance.
Do you agree. Explain

A sheet of copper is placed
between the poles of an
electromagnet with the magnetic
field perpendicular to the sheet.
When it is pulled out, a
considerable force is required,
and the force required increases
with speed. Why?

Obtain solutions as you pass
though the slides

Faraday’s law states that an electric field is
induced in any region of space in which a
magnetic field is changing with time
Strength of the induced field is
proportional to rate of change of inducing
field

Maxwell says - a magnetic field is
induced in any region of space in which
an E is changing with time.
Strength of the induced field is
proportional to rate of change of
inducing field.

Coil – Magnet
Experiment

Closed circuit having a coil and
galvanometer
Move N pole of magnet into the coil
Galvanometer shows deflection
ie. current flow through it
Faraday’s coil – magnet experiment

S pole towards - deflection
opposite.
S pole removed deflection opposite
to S pole introduced.
Deflection is more when magnet is
moving very fast

What is the difference between magnetic flux
and magnetic field?
A loop of wire is place in a uniform magnetic
field . For what orientation of the loop is the
magnetic flux a maximum? For what
orientation is the flux zero?

Faraday’s laws of Eelectromagnetic Induction
i. When ever magnetic flux linked with a
circuit changes emf is induced
ii. Induced emf lasts as long as change in
magnetic flux continues
iii. Induced emf is directly proportional to
rate of change of magnetic flux

Factors affecting the flux
i. Strength of field B
ii. Area A (area is taken as a vector – direction area vector is
normal to area.
iii. Relative orientation of area w.r.to B (θ is the angle
between direction of area vector and magnetic field)
Magnetic flux (φ) = BAN cosθ

is the phenomenon by which a
current is induced in a circuit due
to change in magnetic flux
associated with it
Electromagnetic induction
E M F = -N (dφ/dt)

Fleming’s Right Hand Rule
Father – Mother child? Is it boy or girl?

Direction of induced current
Fleming’s RH rule
Stretch forefinger, middle finger and thumb of
right hand in 3 mutually perpendicular
directions. If the thumb represent direction
of motion of conductor or Force and
forefinger represent direction of Magnetic
field, then middle finger gives the direction
of induced Current .

Lenz’s law

Direction of induced emf in the coil
Lenz’s law
Direction of induced current is such as
to oppose the cause which produces it.
When N pole is moved towards the coil ,
current is induced in such a direction
so that face of the coil near to
approaching N pole will be N pole etc.

Importance of Lenz’s law
Accordance with conservation of energy
For moving the magnet, external agent has
to do work against the forces of
attraction (repulsion as the case may be)
which is getting converted into electrical
energy

Wearing a metal bracelet in a
region of strong magnetic field
could be hazardous. Explain.

A piece of aluminum is dropped
vertically downward between the
poles of an electromagnet. Does
the magnetic field affect the
velocity of the aluminum?

Origin of induced emf?
A current will flow through a metallic conductor if
there is an electric field within it, which will push
the charge carriers through it.
Normally this flow of charge will try to neutralize this
field.
So, an external mechanism is required to maintain.
Work done/unit charge to maintain the field is emf.

Magnetic flux can be changed by
1. Keeping B fixed, moving whole or part of the loop.
2. Keeping loop at rest and changing B
3. Both.
Magnetic flux (φ) = BAN cosθ

1. Motional emf: Keeping B fixed, moving whole or part of
the loop.
2. Induced electric field: Keeping loop at rest and changing
So two different mechanisms by which emf can be induced

Motional EMF
Rectangular loop of which one side is movable (PQ) is placed
in a magnetic field perpendicular to the plane of the loop.
PQ is moving in with a velocity ‘v’.
Situation may be visualized in two ways
1. Magnetc flux associated with the loop is changing or
2. Movable section is breaking the magnetic field lines.
Induced emf = - dφ/dt = -d(B lx)/dt = -Bl dx/dt = -Blv

Motional EMF
As the conductor is moving charge on the section PQ
experience Lorentz force F = qvB (Sinθ = 1)
Work done = F l
EMF = work done/unit charge = Fl/q = qvB l/q = Blv
ie. Faraday’s electromagnetic induction is in
accordance with Lorentz force

A conductor PQ is moving in magnetic field.
R is connected externally to PQ. Applying Fleming’s RH rule,
direction of current will be as shown in fig a.
Free electrons will experience F = qvB.
Moving rod act like a source of emf (so replaced with battery
and internal resistance in fig b)
Current i = Blv/(R+r)

Moving rod act like a source of emf (so replaced with battery
and internal resistance in fig b)
Current can also be determined using Lenz’s law.
φ = B lx
emf = -dφ/dt = Blv

Energy in motional emf
R – resistance of the movable arm PQ .
Current I = V/R = BLv/R
A current carrying conductor in a magnetic field will
experience a force F = B I L = B (BLv/R) L
= B2L2v/R
(capital letter L is used to avoid confusion with current I)
Power required to push the arm with constant speed
P = F v = B2L2v2/R
Joule loss in the conductor PJ = I2R = B2L2v2/R
ie.mechanical energy used to push the arm PQ is
converted into electrical energy.

The length of the wing of a jet plane is 20 m. The plane is
moving in the morth south direction with a velocity of 1620
km/h at a phace where the dip angle is 40o. If the earth’s
horizontal field at the palace has a magnitude of 0.4 x 10-4 T.
Calculate the emf induced in the wing?
Hint: v = 450 m/s
Bv = Bhtanθ = 0.336 x 10-4 T
Emf = Bv l v

A wheel has 10 metal spokes each having a length of 1m. It
rotates in a magnetic field of flux density 0.4 x 10-4 T, applied
normal to the plane of the wheel. If an emf of 0.1 V is induced
between the rim and the axis, find the number of rotations
per second of the wheel.
Hint: EMF = -dφ/dt = -BdA/dt (here flux change is due to change
in area)
When the wheel makes one rotation, Area = πl2.
No. of revolutions/sec = frequency ?
dA/dt = area x frequency
Emf = -B A frequency.

A rectangular loop of sides 15 cm and 5 cm is placed
perpendicular to a uniform magnetic field of strength 0.4 x
10-4 T. In 0.25s the loop is change to a square and flux density
is increases to 0.8 x 10-2 T. Calculate induced emf?
Hint: EMF = -dφ/dt = (φ2-φ1)/t
Perimeter is same in both shapes.
φ= B A

A coil of wire containing 500 circular loops with
radius 4.00 cm is placed between the poles of a
large electromagnet, where the magnetic field
is uniform and at an angle of 60o with the plane
of the coil. The field decreases at a rate of 0.200
T/s. What are the magnitude and direction of
the induced emf?
Hint; Given dB/dt = -2 T/s
dφ/dt = (dB/dt) A cos 30o.
Emf = -Ndφ/dt = 0.435 V Dr. Pius Augustine, S H College, Kochi

Homopolar or Faraday Disc Generator
Cu disc is rotated about the axle X
in a perpendicular magnetic field.
Y- point on circumference
EMF is induced between X and Y (A and B)
Consider a line segment XY
Velocity of the point X = 0 and Vy = ωR
ω –angular velocity.

Homopolar or Faraday Disc Generator
Since velocity is a variable from point X to Y.
Imagine a small element on the assumed XY as dr, having
radius r.
Induced emf on dr = B dr ωr
Total emf of the line segment XY = integrate the above over
the limit 0 to R Which will give
EMF = ½ BωR2 = BπR2f
ω = 2πf
Output voltage will be a dc voltage.

Sign rules for direction of induced emf
1. Define a positive direction for the area vector (A)
2. From the direction of area vector (A) and the
magnetic field (B) determine the sign of magnetic
flux φ.
3. Determine the sign of induced emf or current
[If the flux is increasing, dφ/dt (emf or current) is
positive and vice versa]

4. Direction using right hand. Curl the fingers of
your right hand around the area vector (A),
with your thumb in the direction of area
vector.
5. If the induced current of emf is +ve, it will be
in the direction of your curled fingers and if –
ve, opposite.

A copper disc of 10 cm radius is ratating at 20
rps about its axis with its plane perpendicular to
a uniform field of flux density 0.4 Wb/m2. What
is emf induced between the rim and the centre?
EMF = ½ BωR2 = BπR2f
ω = 2πf

Eddy Currents (Foucault’s current)
• Loops of electrical current induced within
conductors by a changing magnetic field in the
conductor according to Faraday's law of induction.
• Eddy currents flow in closed loops (path of least
resistance) within conductors, in planes
perpendicular to the magnetic field.

Eddy Currents (Foucault’s current)
• Eddy currents dissipate energy – undesirable
• Cores of transformers and dynamos- layers
separated by insulating material like lacqueer – to
increase resistance and decrease eddy currents

Uses - Eddy Currents (Foucault’s current)
• Speedometers
• Induction furnace
• Braking system

How would you demonstrate that a
momentary current can be obtained by
the suitable use of a magnet and a coil
of wire ?
What is the source of energy associated
with the current so obtained ?

Explain why induced current must flow in
such a direction so as to oppose the
change producing it ?
Explain the significance of Lenz’s law to
show the conservation of energy in
electromagnetic induction .

Identical coils one Cu and other Al are
given identical change in magnetic
flux.
Will there be any difference in induced
emf or induced current? Explain

What is Electromagnetic induction ?
Describe one experiment to demonstrate
the phenomenon of electromagnetic
induction

What kind of energy change takes place
when a magnet is moved towards a coil
having a galvanometer at its ends ? Name
the phenomenon

A magnet is plunge in and out of a closed loop
of rubber. Will there be emf induced?
What about induced current?
Emf will be induced like a metal loop.
No induced current as electrons in rubber are
tightly bound to the atoms.

Note : changing a magnetic field in
a closed loop induces current. If
the loop is in an electrical
conductor (or open loop) then
voltage is induced.

Note: i. conductor moved parallel to
the field, there is no change in the
magnetic flux and no induced current
Conductor moved perpendicular to B,
maximum flux is broken and
maximum induced emf will be
produced. Dr. Pius Augustine, S H College, Kochi

Note: A circular and a rectangular coil
moving with uniform velocity in a
normal B, emf induced is uniform in
rectangular coil, non uniform in
circular coil

State two factors on which the
magnitude of induced emf depend.
i. Number of loops
ii.Rate at which the magnetic field changes
within those loops.

State two factors on which the magnitude
of induced current depend.
i. Induced voltage
ii.Resistance of the coil and circuit to
which it is connected.

Describe briefly one way of producing an
induced current, state on factor that
determines the magnitude of induced emf.
What factor determines the direction of
induced emf ?

Why is it more difficult to move a
magnet towards a coil which has
large number of turns ?
Induced emf is more when no. of turns is more.

Applications of EMI
On the road – EMI triggers traffic light
when car drives over coils (which changes
magnetic field) of wire beneath the road
surface ( USA) .

Applications of EMI
Hybrid cars utilize
it to convert
braking energy
into electric
energy in their
batteries.

Applications of EMI
ATM : magnetic strip is
swiped through scanner.
A credit card’s number, expiration date, and card holder name
are coded into a magnetized pattern in a stripe on the back.
When the card is ‘swiped’ the moving stripe bathes the
reader’s circuitry in a varying magnetic field that induced
currents in the circuits, which transmit the information in the
stripe to the cardholder’s bank

Applications of EMI
Security system in airport: we walk
through upright coils. If we carry
significant quantities of iron, change
the magnetic filed of coils and trigger
an alarm.
Security check point generates an alternating magnetic field,
which induces an eddy current on metal objects with the
passenger.
Eddy current in turn produce an alternating magnetic field,
which induce a current in detectors reciever’s coilDr. Pius Augustine, S H College, Kochi

Applications of EMI
Guitar pick ups: tiny coils with magnets
inside them. The magnets magnetize the
steel strings. When the strings vibrate ,
voltage is induced in the coils and
boosted by an amplifier.

What happens when a magnetically
stored bit of information on a
computer disk spins under a reading
head that contains a small coil?
Changing magnetic field in the coil
induces voltage.
Information stored is converted to
electric signal.

Transformer
Based on mutual induction
Works only in AC
Low voltage high current to
high voltage low current or
reverse.

Can a transformer work when it is
connected to a dc source ?

Iron has large magnetic permeability and helps
in bringing field lines in one coil due to current,
almost completely within the entire core)
Two coils wound around core of soft iron?
Iron core reduces hysterisis loss during repeated
cycle of magnetization and demagnetization

Why soft iron generally used as the core of
the electromagnet?
i. less retentivity - can be magnetised and
demagnetised easily
ii. High permeability – intensifies magnetic
field inside.
iii. Hysterisis loss is minimum.

Transformer – works based on Mutual Induction
A device that transfers electrical energy from one circuit to
another through inductively coupled coils.
A varying current in the first or primary winding creates a
varying magnetic flux in the core and thus a varying magnetic
field through the secondary winding.
• Electromotive force (EMF) or "voltage" is induced in
secondary winding

Principle of Transformer
Two principles:
1. An electric current can produce a magnetic field
(electromagnetism)
2. A changing magnetic field within a coil of wire induces a
voltage across the ends of the coil (electromagnetic
induction).
Changing the current in the primary coil changes the magnetic
flux developed.
The changing magnetic flux induces a voltage in the secondary
coil. Dr. Pius Augustine, S H College, Kochi

Types of Transformer- Step Up Transformer
Allows an alternating current (AC) voltage to be
"stepped up“
Ns greater than Np.
Secondary voltage is greater than primary voltage
Secondary current is less than primary current

Draw a labeled diagram to show the
various components of a step up
transformer ?

Types of Transformer - Step down Transformer
Allows an alternating current (AC) voltage to be
"stepped down“
Ns less than Np.
Secondary voltage is less than primary voltage
Secondary current is more than primary current

Describe a step down transformer and
explain how it works. State two
characteristics of the primary coil as
compared to its secondary coil.

Primary -The winding to which power is
supplied
Secondary – from which power is delivered
Es/Ep = Ns/ Np = Ip / Is
Ns/ Np - turn ratio of transformer
Ideal transformer Pin = Pout .
Ep Ip = Es Is Dr. Pius Augustine, S H College, Kochi

Efficiency of a transformer η
η = output power/input power
If multiplied by 100 – will give %
efficiency
η = EsIs/EpIp

A transformer steps up 120 V to 4800
V. The current in its primary and
secondary are 5A and 0.1 A
respectively. Find efficiency?
η = EsIs/EpIp
= 0.8
80 %

When 100V a.c is applied across the
primary of a transformer, the current in the
primary and secondary units are 2 A and
0.2 A respectively. If the transformer has
efficiency of 90% find the voltage across
the secondary.
η = EsIs/EpIp
= 0.9
Ans: 900 V

How are the emf in the primary and
secondary coils of a transformer
related with the number of turns in
these coils ?

Step up
Ns > Np
Transformer diagram
Es > Ep
Ip > Is
Turn ratio > 1
Signal diagram
Step down
Ns < Np
Transformer diagram
Es < Ep
Ip < Is
Turn ratio < 1
Signal diagram

A step down transformer operates at 220 V
is used to supply a current of 0.4 A to a 20
W bulb. If its secondary has 50 turns, find
the current in the primary and the number
of turn of the primary coil.
Ans: 0.09 A 220

Draw a labeled diagram of a device you
would use to transform 200V a.c to 15 V
a.c.
Name the device and explain how does it
work.
Give its two uses.

In the case of transformer input and output
are out of phase by 180o. Give reason
Hint: Lenz’s law
Primary is the inducing voltage and secondary –it is
induced voltage

Factors determine the magnitude of
induced emf of secondary coil
i. Turn ratio
ii. Primary voltage

Energy losses in transformer
i. Copper loss or Joule loss (H=I2Rt)
ii. Magnetic hysterisis loss
iii.Eddy current loss (lamination to
minimise)
iv.Flux leakage

Uses of transformer
i. In electric grids (power transmission)
ii. Step up – X ray tube, TV
iii. Step down - electric bells , battery charger ,
radio etc.
iv. Step up cum step down is used in fridges, TV
etc.

Uses of Step Up Transformer
1. Electric power transmission at the power
generating station
2. Television and wireless sets
3. Within X-ray tubes to provide high
accelerating voltage

Uses of Step Down Transformer
1. With electric bells
2. With radio sets
3. At power grid station
the voltage before its
distribution to the
consumer

For what purpose are transformers
used ?
Can they be used with a direct current
source ?
Hint: dc will not produce change in magnetic flux

Unit of magnetic flux is weber
And magnetic field (magnetic flux density)
B is weber/m2 or tesla (T)

A C Generator

AC dynamo or Turbo generator
Converts mechanical energy into
electrical energy
Based on EM induction
Faraday’s laws

Construction
i. Armature: Rectangular coil consists
of large no. of turns wound over a
soft iron core capable of rotation
about an axis passing through it

ii. Field Magnet: provides
uniform magnetic field.
For small dynamos – use
permanent magnets and in big
dynamos use electromagnets.

iii. Slip rings: Free ends of armature
coil are connected to two rings S1
and S2 which rotate along with
armature about the same axle

iv. Brushes: Slip rings slide against
stationary contacts of carbon
called brushes which act as o/p of
the generator.

alternator

Atomic explanation for electromagnetic induction
When wires of spinning armature cut through
the magnetic field, oppositely directed
electromagnetic forces act on the –ve and +ve
charges.
ie: electrons experience force in one direction
and copper atoms (+ve ions) in opposite.

Atomic explanation for electromagnetic induction
Since ions are anchored in the lattice, only
electrons move, sloshing back and forth in
alternating fashion with each rotation of
the armature.
Energy of the sloshing electrons is the ac
o/p.

Working
As coil rotates in magnetic field (by external means)
flux associated with the coil changes continuously
and induces emf
Fig i. side AB moves out of plane of paper and CD into
paper
A
B C
DDr. Pius Augustine, S H College, Kochi

Sides BC and AD will not cut magnetic field
lines and hence will not induce emf.
Apply Fleming’s Right Hand rule -
induced current flows from B to A and D to
C and o/p is from (A to D)

Second half rotation – positions of AB
and CD interchanged and direction of
induced current is from D to A

Since induced current continuously
changes in magnitude and direction
changes after every half rotation,
it is a.c.

Note. ii. Magnitude of emf is maximum
when flux change is maximum.
This happens when the coil just comes
parallel to B in its rotation
(even if the coil turns by small angular
displacement, it would break the field
lines)

So, in one complete rotation of the coil emf
induced is maximum twice when the coil
comes parallel to the magnetic field and
induced emf will be minimum twice
when the coil comes perpendicular to the
magnetic field.

Another way
φ = BAN cosωt.
B – magnetic field
A – area of the coil
N- number of turns of the coil
ω – angular velocity of roation
θ = ωt is the angle between area vector and
magnetic field.
Area vector is perpendicular to area. Fig θ = 90o
Induced emf = -dφ/dt = BANω sinωt.
A
B C
D

Induced emf = -dφ/dt = BANω sinθ.
Analyze one complete rotation.
θ = 0, emf = 0
θ = 90, emf = BANω
θ = 180, emf = 0
θ = 270, emf = - BANω
θ = 360, emf = 0
Caution!!
θ is the angle between
normal to the coil
(direction of area vector)
and magnetic field

Note. i. alternating emf produced
has the frequency same as
frequency of rotation of coil.

In an a.c .generator the speed at which the
coil rotates is doubled. How would this
affect i) the frequency of o/p voltage ii)
maximum o/p voltage.
Hint: Emf = BANω sinωt θ = ωt

State the principle of simple ac generator ?
What determines the frequency of a.c
produced in a generator?
Draw a labeled diagram of a simple a.c
generator Dr. Pius Augustine, S H College, Kochi

What is the effect on the magnitude of emf
generated in an a.c. generator if the
speed of rotation of the coil of generator
is increased ?

Suggest two ways to produce a higher
emf in an a.c. generator?

i. ME to electrical
ii. Principle – EM
induction.
iii. ME is used to
rotate armature.
iv. Use two separate
slip rings
i. EE to ME
ii. Torque experienced
by a coil in B
iii. Electrical energy to
provide torque for
rotating the coil.
iv. Use two split rings
act as commutator
ac generator vs dc motor

What energy conservation takes
place in a generator ?

A long, straight conductor passes through
the center of a metal ring, perpendicular
to its plane. If the current in the
conductor increases, is a current induced
in the ring? Explain.

Two circular loops lie side-by-side in the same
plane. One is connected to a source that
supplies an increasing current; the other is a
simple closed ring. Is the induced current in
the ring in the same direction as that in the
loop connected to the source, or opposite?
What if the current in the first loop is
decreasing Explain.

A loop of wire enclosing an area A, is placed in a
region where the magnetic field is
perpendicular to the plane of the loop. The
magnitude of B varies in time according to the
expression B = Bmaxe-at, where a is some
constant. That is at t=0 the fies is Bmax and for
t>0 the field decreases exponentially. Find the
induced emf in the loop as a funciton of time

For my youtube videos: please visit -
SH vision youtube channel
or
xray diffraction series
SH Vision
Dr. Pius Augustine, SH College, Kochi

123
Appeal: Please Contribute to Prime Minister’s or Chief
Minister’s fund in the fight against COVID-19
Dr. Pius Augustine, Dept of Physics, Sacred Heart College, Thevara
we will
overcome
Thank You
http://piusaugustine.shcollege.ac.in
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Dr. Pius Augustine, Asst. Professor, Sacred Heart College, Thevara, Kochi.

24 pius augustine em induction & ac

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