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Electromagnetic Induction
Faraday: “ convert magnetism into electricity”
What we know…
• Current in a wire generates magnetic field
• Field of a solenoid is similar to that of a bar
magnet
• Strength of magnetic field depends on
permeability ( magnetic properties of magnet)
• Interaction between magnetic field and electric
field results in a magnetic force ( as in electric
motor)
Can a magnetic field induce a current in a wire?
Electromagnetic induction
Electromagnetic induction is the process
of generating current by:
- moving a wire through a magnetic field, or
-moving a magnetic field across a wire
( conductor)
[ relative motion between the magnetic field and
a wire]
Michael Faraday’s Experiment
Closed loop of wire ( attached to galvanometer) is placed in a
magnetic field
No current
Current
is generated
generatedininwire
wireif:if:
-Wire is
moves
stationary
relative
( not
to the
moving)
magnetic field
-Wire moves perpendicular
parallel to magnetic
to magnetic
field field
( maximum current generated)
Direction of the current
When the direction of magnetic
field changes, the direction of the
current changes
How can you tell the direction of the current?
4th Right Hand Rule
Palmdirection of current
(Force on the charge)
Fingersmagnetic field (B)
Thumb –
direction the wire moves ( velocity)
To determine the force on a charge or direction of
conventional current
Use the 4th Right Hand Rule to find the direction
of the induced current in this wire
If the wire moves to the right, in which
direction does the induced current
move?
In what direction should the
wire be moved, relative to the
magnetic field to generate the
minimum voltage?
0 voltage - Parallel to magnetic field
Electromotive Force (EMF)
Measured in Volts (V)
Makes current flow from lower to higher potential
Wire moves through a
magnetic field
Force is exerted on a charge
in the wire
Electrical Potential
energy increases
Charge moves in the direction
of the force = work is done
Difference in potential is called induced EMF
EMF is the Potential Difference across a wire moving in a
magnetic field ( or voltage given to a charge by a battery)
EMF depends on:
-velocity of the wire,
[v]
- the length of the wire [L]
- the magnetic field,
[B]
EMF = BLv( sin θ)
[ sin θ – if wire in not
perpendicular to magnetic fieldfind the perpendicular
component of the velocity]
The Current induced in the wire depends on:
- v, L B and resistance in the wire
V= Voltage
v= velocity
Units of EMF
• EMF = BLv
N
m
xmx
=
Am
s
=
Nm
As
=
J
= Volts
C
units
Q= It
C= As
W=Fxd
J=Nm
Potential energy is work done per unit charge = J/C = Volts
Solve 1
• A 20m long wire moves at 4m/s at an angle of
450 through a magnetic field. An EMF of 40V
is induced in the wire. What is the strength of
the magnetic field?
EMF = BLv sinθ
40V = B x 20 x 4 x sin 45
B = 0.707 T
Solve 2
calculations
L
A straight wire, 0.30 m long, moves at a constant
v
B
900
speed of 10.0 m/s perpendicular to a 0.20-T
magnetic field.
a. What is the induced EMF in the wire?
EMF = Blvsinθ
= 0.2 x 0.3 x 10 sin 90
= 0.6V
b. What is the current in the wire if it is part of a
circuit with a resistance of 25Ω ?
V =IxR
0.6 = I x 25
R
• What is the induced emf in a wire 0.5m
long moving at right angles to a 0.04T
magnetic field with a velocity of 5m/s?
0.1
Challenge
A square wire loop moves perpendicularly through a magnetic
field of strength 1.75 T at a velocity of 2.5 m/s,
The direction of the magnetic field is out of the page.
1. If the wire loop is 10 cm on a side, calculate the magnitude of
the induced electromotive force in the wire segment:
EMF = Blvsin 90
a.
AB.
Use 4th right hand rule – EMF = 0V
b.
BC.
c.
CD.
No magnetic field – EMF = 0V
d. With a total resistance of 130 Ω, calculate the induced current
in the wire loop.
Complete exercise pg 675 no. 1-4
A: 0 degrees
D
D
B: 90 degrees
B
C
B
C
A
B
A
D
B
A
D
A
C: 180 degrees
C
C
D: 270 degrees
In which of these will maximum EMF be induced?
A and C
Application of induced EMF
e.g. Microphone
Application of induced EMF
a diaphragm in a microphone is
attached to a coil of wire that is
free to move in a magnetic field.
1. Sound waves vibrate the
diaphragm
2. This moves the coil in the
magnetic field.
3. The motion of the coil induces an
EMF across the ends of the coil.
• Voltage can be increased by
electronic devices
How is an EMF produced in a microphone
Sound wave converted to electrical signal
The induced EMF varies as the frequency of the sound varies.
This converts sound energy to electrical signal
Magnetic flux
• Magnetic flux is the number of magnetic
field lines passing through a surface
placed in a magnetic field.
Magnetic flux and Faraday’s law of
Induction
An external magnetic field passes through a region at an angle θ
to the region
Perpendicular component
of magnetic field = Bcosθ
Magnetic
field
θ
area
Magnetic flux Φ is the product of the perpendicular component of
the magnetic field and cross sectional area A
Magnetic flux and Faraday’s law of
Induction
Φ = BA cos θ
Φ = magnetic flux
B = magnetic field strength
A = cross sectional area
Weber (Wb)
Tesla (T)
(m2)
1 Wb = 1 T.m2
Magnetic flux Φ is the product of the perpendicular component of
the magnetic field and cross sectional area A
Perpendicular to
surface
Perpendicular to
surface
Magnetic field lines
perpendicular to
Surface
Flux is maximum
Φ = BA cos 0
= BA
Magnetic field lines
parallel to surface
Flux is 0
Φ = BA cos 90
=0
The circular loop in the figure
has a radius of 4 cm and
makes an angle of 230 with a
2-T magnetic field. What is
the flux through the loop?
Φ = BA cos θ
A = πr2
2
-3
=
π
(4/100)
= 2 x (5 x 10 ) cos 23
= 5 x 10-3 m2
= 9 x 10-3Wb
A square with sides of length 2 m is perpendicular to a
magnetic field of strength 10 T. If the square is rotated
by 60º, what is the change in magnetic flux through the
square?
=BA cos θ
-
 = BA cosθ
= 10 x 2 x 2 x cos 0
-
10 x 2 x 2 x cos 600
= 40
-
= 20 Wb
20
Magnetic field strength
Magnetic flux density = magnetic flux per cross sectional area
= Wb/m2

magnetic flux density 
A
Φ = BA
Φ/A = B ( magnetic field strength)
= magnetic flux density
Faraday’s law of Induction :
Induced motional EMF is due to the rate of change of the
magnetic flux
ΔΦ
emf  
Δt
If a coil has a number of turns use the equation:
ΔΦ
emf   N
Δt
problem
A coil is made of 10 turns of wire and has a
diameter of 5cm. The coil is passing through
the field in such a way that the axis of the coil
is parallel to the field. The strength of the field
is 0.5T.
a. What is the change in the magnetic flux?
B. If an average EMF of 2V is observed, for
how long was the flux changing?
-9.8 x 10-4
4.9 x 10-3s
recap:
1. What is the induced EMF in a wire that is 20 cm
long, moving at an angle of 300 to a 0.08 T
magnetic field with a velocity of 5 m/s
2. A flat 300 turn coil has a resistance of 3Ώ. The
coil covers an area of 15cm2.
At what rate must the magnetic field change in
order to induce a current of 0.75 A in the coil? ( find
the rate of change of magnetic field)
EMF = I x R
ΔΦ
emf   N
Δt
Φ = BA cos θ
EMF = BLv( sin θ)
Electrical generators
Pg 675 PPP
Electrical generators
• Invented by MICHAEL FARADAY
• Electrical generators change mechanical energy to electrical
energy
Made up of:
Wire loop placed in
How an electric generator works
Magnetic field
The armature rotates in the
magnetic field
When the wire is perpendicular to
magnetic field, it cuts the
magnetic field- EMF induced
To determine the direction of the induced
current – use 4th right hand rule
To increase the strength
of the magnetic field:
1. Wire is wound around
an iron core – called an
armature
To increase the induced EMF:
- Increase the length of the coil by
increasing the number of turns
How does the strength and direction of the current change?
Wire is perpendicular
to magnetic field
When coil is horizontal ( 900 to
magnetic field)
Maximum EMF induced
Wire is parallel to
magnetic field
When coil is vertical (00 to magnetic
field)
Minimum (0) EMF induced
When is maximum current produced?
EMF is not induced in
this side of the coil
(AB or CD)
A
D
Using the 4th right hand rule
We see that the current will
move to the side of the wire- no
EMF induced.
B
C
if the coil moves clockwise ( as shown),
current moves anticlockwise ( use right
hand rule)
Magnetic field reverses direction every
½ turn- produce alternating current
EMF induced = BLv(sinθ)
L= AD or BC
Is current induced in all sides of the loop?
Voltage-time graph for ac current
Equation for this graph:
V= Vmax cos 2πft
f = frequency of alternation
How can we increase the
frequency of a generator?
Increase the number of magnetic pole pairs
Motors and Generators
Converts electrical energy to
mechanical energy
Converts mechanical energy
to electrical energy
Voltage is placed across an
armature in a magnetic field
Mechanical energy turns
armature in a magnetic field.
Voltage cause current to flow
in the coil- armature turns
Induced voltage cause
current to flow
Electric generator
Made up of a number of wire loops
placed in a strong magnetic field
to increase the
strength of the
magnetic field,
wire is wound
around an iron
core (armature)
which rotates
freely
As the armature
turns, the wire
loops cut
through the
magnetic field
lines and
induce an EMF.
EMF depends on the length of wire.
Increasing the number of loops in the armature increases the
wire length,
the induced EMF produces an electric current
magnetic field induces an EMF.
Electric generators
http://www.animations.physics.unsw.edu.au/jw/electricmotors.html#DCmotors
Explain the construction and
working of an AC generator
• Principle
When a straight conductor is moved in a
magnetic field, then a current is induced in
the conductor.
• It is based on electromagnetic induction.
Explain the construction and
working of an AC generator
Made up of
Permanent magnets
armature
brush & slip-rings:
allows the armature to
turn freely and allows the
current to pass into the
external circuit
made up of a
number of turns
of wire on a soft
iron core
•An energy source turns the armature at a fixed
frequency. E.g. 60Hz in US, 50Hz - UAE
Alternating current AC generators
The Current changes direction
in the external circuit
• As the armature turns, the
alternating current varies
between a maximum value
and zero
• How is the AC generator
different from a motor?
• As the armature turns the velocity vector perpendicular
to the magnetic field changes.
The flux changes continuously with time
This change in magnetic flux induces an emf
The direction of the induced emf is reversed after every
half rotation of the coil.
Thus in one rotation of the coil, the current changes its
direction twice in the coil
Average power
The power produced by a generator is the product of the current
and the voltage.
P=IxV
• power varies because both
current and voltage vary.
• Power is always positive because
I and V are either both positive or
both negative.
DC generators
Split ring commutators :
Act as full-wave rectifiers
change the alternating current in the coil to DC in the external circuit
AC generator
DC generator
Similarities: Both change mechanical energy to electric energy
both have commutators with brushes, magnetic field with armature
Differences:
1. 2 Slip rings which causes AC current in
the external circuit
1. Has split rings which changes AC
current in the internal circuit to DC in
external circuit- act as full wave rectifier.
( Diodes also act as rectifiers)
Average power
PAC, is half the maximum power
Effective current
P = I2R
If we express AC POWER in terms of effective current, then
PAC = I2eff R
But PAC = ½ PACmax
I2eff R = ½ I2max R
I eff
2

I max
2
Ieff = 0.707 Imax
Effective Voltage
• Effective voltage, known as RMS (root
mean square) voltage. ( In US – 120V, in
UAE- 220V).
• Why is effective current ( voltage) less
than the maximum value?
In AC generators, power varies from a maximum to
zero value.
The effective current ( voltage) is a constant value of
current that would cause the average power to be
dissipated
formulae
Ieff = 0.707 Imax
Veff = 0.707 Vmax
http://www.thatquiz.org/tq/classpage?0010123468a4d03