Lesson 18
Chin-Sung Lin
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In 1831, Michael Faraday (England) and
Joseph Henry (US) independently discovered
that magnetism could produce current in a
wire
Faraday’s law— Electromagnetic induction
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Electromagnetic induction— any change in
the magnetic field around a conductor
induces a voltage (or emf)
Faraday’s law— The induced voltage (or
emf) in a coil is proportional to the product
of the number of loops and the rate of
change of the magnetic field within those
loops
How can we change the magnetic field
around a conductor to induces a voltage (or
emf)?

The change could be
produced by
◦ relative motion of a wire with
respect to the magnetic field
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The change could be produced by
◦ moving the coil into or out of the
magnetic field
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The change could be produced by
◦ rotating the coil relative to the magnet
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The change could be produced by
◦ changing the magnetic field strength
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A magnet moving past a stationary conductor,
or
A conductor moving through a stationary
magnetic field

The work done to the magnet is equal to the
energy generated in the circuit to which the
coil is connected
Wmechanical = Welectric
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Induced voltage depends on:
◦ Speed of the wire traversing the magnetic
field lines. Quicker motion induces a greater
voltage (V ~ v)
◦ Number of loops of wire that moves in a
magnetic field. The voltage is proportional to
the number of loops (V ~ N)
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If the coil does not form a complete circuit,
what will happen?

Induced voltage without current, no work to
plunge the magnet into the coil
-
+

If the coil forms a complete circuit, what is
the direction of the induced current?
A
Ammeter

The induced magnetic field is repelling, the
current will flow in a way to create such a
repelling field
A
Ammeter
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The more loops of the coil, the more voltage
induced (V ~ N)
The more voltage induced in the coil, the more
current through the resistor in the circuit (I ~ V)
The more current through the coil, the stronger
the magnetic field it generated (B ~ I)
The stronger the magnetic field generated, the
stronger the repelling force acting back to your
magnet (F ~ B)
A coil with more loops is a stronger electromagnet
and push back harder

What factors will affect the induced current?
A
Ammeter

Induced current depends on
◦ the induced voltage
◦ the resistance of the coil and the
◦ the “reactance” of the coil
A
Ammeter

Reactance
◦ similar to resistance
◦ depends on
 the number of loops in the coil
 the frequency of the AC source

Reactance
The counter-emf is the source of the
opposition to current flow change
◦ A constant DC current has a zero rate-ofchange, and sees an inductor as a shortcircuit
◦ An AC current has a time-averaged rateof-change that is proportional to
frequency, this causes the increase in
inductive reactance with frequency

Induced voltage of a moving
conductor in a magnetic
field
V=vBL
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The movement of a magnet is alternating,
the induced voltage alternates on direction
The greater the frequency of the field
change, the greater the induced voltage

The frequency of the induced alternating
voltage equals the frequency of the
alternating magnetic field within the loops
High Frequency
Low Frequency
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Generator— a device that converts

Motor— a device that converts electrical
mechanical energy to electrical energy
energy to mechanical energy
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When a closed conductor loop is moved in a
magnetic field, an induced current flows
through it
The direction of induced current is given by
the Flemming's right hand generator rule

What’s the direction of the induced current?
N
S

Given by the Flemming's right hand generator
rule
N
S
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As the number of magnetic field lines within
the loop changes, the magnitude and direction
of the induced voltage and current change

One complete rotation of the loop produces
on complete cycle in voltage and current
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The voltage induced by the generator
alternates, and the current produced is
alternating current (AC)
The standard alternating current is 60 Hz

Hydro power
generators
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A a static device that transfers electrical
energy from one circuit to another through
inductively coupled conductors
A static device that transfers electrical energy
to magnetic energy, and to electric energy
again
A device with which we can raise (for
transmission) and lower (for use) the AC
voltage in a circuit
Transformer only works for AC
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Primary and secondary coils
Use AC voltage source (primary coil)
AC voltage is induced (secondary coil)
Frequency AC voltage source = Frequency Induced AC voltage
Primary
Secondary
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Iron core (high permeability) is inserted into the
coils to intensify the magnetic field
Iron core forms a complete loop to guide all
magnetic field lines through the secondary
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Transformer Symbol:
IS
IP
Np
Ns
Vp
Vs
Ip
Is
no. of turns of primary coil
no. of turns of secondary coil
voltage of primary coil
voltage of secondary coil
current of primary coil
current of secondary coil
IS
IP
VP
VS
=
NP
NS
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Step-up transformer
◦ NP < NS
◦ VP < VS

Step-down
transformer
◦ NP > NS
◦ VP > VS
IS
IP
PP = PS
IP VP = IS VS

VP / NP = VS / NS

IP VP = IS VS

VP / VS = IS / IP = NP / NS

VS = VP (NS / NP )

IS = IP (NP / NS )
VP
IS
NP
=
=
VS
IP
NS
VS = VP
NS
NP
NP
IS = IP
NS

Faraday’s law:
◦ An electric field is created in any region of space in
which a magnetic field is changing with time
◦ The magnitude of the created electric field is
proportional to the rate at which the magnetic field
changes
◦ The direction of the created electric field is at right
angles to the changing magnetic field

Maxwell’s law:
◦ A magnetic field is created in any region of space
in which an electric field is changing with time
◦ The magnitude of the created magnetic field is
proportional to the rate at which the electric field
changes
◦ The direction of the created magnetic field is at
right angles to the changing electric field

In 1861 Scottish physicist
James Clerk Maxwell
discovered the theory of
electromagnetism

Maxwell united all
previously unrelated
observations and equations
of electricity, magnetism
and optics into a consistent
electromagnetic field theory

German physicist Heinrich
Rudolf Hertz was the first to
satisfactorily demonstrate the
existence of electromagnetic
waves by building an
apparatus to produce and
detect VHF or UHF radio
waves

A charge oscillates back and forth in empty
space will produce electromagnetic waves in
space where vibrating electric and magnetic
fields regenerate each other

Electric field is perpendicular to the magnetic
field, and both are perpendicular to the
direction of the motion of the wave
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No medium is required
The speed— the speed of light
The wave is continuously self-reinforcing. The
changing electric field induced a magnetic field.
The changing magnetic field acts back to induce
a electric field