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Chapter 21
Magnetic Induction
and Chapter 22.9: Transformers
Magnetic Induction
 Faraday’s Law
 “A changing magnetic flux
induces an electromotive
force (emf)”
 B
ε
t
 Lenz’s Law
 “the magnetic field
produced by an induced
current always opposes any
changes in the magnetic
flux”
Example: Falling Magnet
 Suppose a bar magnet
falls downward through a
loop of wire, north pole
first.
v
N
v
S
 What is the direction of the
induced current?
 Suppose a bar magnet
falls upward through a
loop of wire, south pole
first.
 What is the direction of the
induced current?
Inductance
 Consider the circuit
shown
 When the switch is
closed
 Current flows through the
solenoid and produces a
magnetic field
 The magnetic field changes
the flux through the solenoid
 The changing flux induces
an emf to oppose the
change in flux
Inductance, cont.
 Induced emf acts like a battery pushing current in the opposite
direction
 This phenomenon is called self-inductance (or inductance)
 The current changing through a coil induces a current in the
same coil
 The induced current opposes the original applied current, from
Lenz’s Law
Section 21.4
Inductance of a Solenoid
 Faraday’s law can be used to find the inductance of
a solenoid
 L is the symbol for inductance
 The unit of inductance is the henry

1H=1V.s/A
 The voltage across the solenoid can be expressed in
terms of inductance
Section 21.4
Inductor
 The principle applies to all coils or loops of wire
 The value of L depends on the physical size and
shape of the circuit element
 The circuit element that uses self-inductance is
called an inductor
Section 21.4
Inductor, cont.
 The voltage drop across an inductor is
I
VL  L
t
 Whenever the current through an inductor changes,
a voltage is induced in the inductor that opposes this
change
 Many inductors are constructed as small solenoids
 Almost any coil or loop will act as an inductor
Section 21.4
Real Inductors
 Most practical inductors are made by wrapping a
wire coil around a magnetic material
 The magnetic material increases the inductance
 Magnetic material has greater permeability than free
space
 Most inductors contain a material that produces a
larger L in a smaller package
Section 21.5
RL Circuit
 An RL Circuit is a circuit composed of
any number of resistors, inductors, and
voltage sources
 Combined with capacitors, they form
RLC Circuits
 RLC circuits can describe almost
any electronic circuit
 RLC circuits are discussed in Chapter 22
Section 21.5
RL Circuit, cont.
 Before switch is closed,
 No current flows (open circuit) so
I=0
 No current suggests no potential
difference across circuit components
 VR = 0
 VL = 0
Section 21.5
RL Circuit, cont.
 When switch is closed (t = 0),
 Inductor keeps current at same
value it was before so I = 0
 No current in the resistor means
no potential difference across
the resistor
 VR = 0
 Kirchhoff’s loop rule
indicates

VL = V
Section 21.5
RL Circuit, cont.
 After a long time (t = ∞),
 Back emf from inductor
decreases until there is no
change in the current
 VL = 0
 Kirchhoff’s loop rule indicates
 VR = V
 All the voltage change is
across the resistor

I=V/R
Section 21.5
RL Circuit, cont.
 Because the inductor opposes
any change in current, a
similar phenomenon occurs
when the switch is opened
Section 21.5
Time Constant for RL Circuit
 The current at time t is found by

V
t
I
1 e τ
R

 For a single resistor in series with a
single inductor,
 The voltage is given by VL = V e-t/τ
Section 21.5
Energy in an Inductor
 Energy is stored in the magnetic field of an inductor
 The energy stored in an inductor is
 Very similar in form to the energy stored in the electric
field of a capacitor
 The expression for energy stored in a solenoid is
Section 21.6
Magnetic Energy Density
 Energy contained in the magnetic field actually exists
anywhere there is a magnetic field, not just in a
solenoid
 Can exist in “empty” space
 The potential energy can also be expressed in terms
of the energy density in the magnetic field
PEmag
1 2
energy density  umag 

B
volume 2μo
 This expression is similar to the energy density
contained in an electric field
Section 21.6
Induction Puzzle
 Consider a very long solenoid
is inserted at the center of a
single loop of wire
 The field from the solenoid at
the outer loop is essentially
zero
 Resolution leads to
electromagnetic waves
(Chapter 23)
Section 21.8
Mutual Inductance
 It is possible for the
magnetic field of one
coil to produce an
induced current in a
second coil
 The coils are connected
indirectly through the
magnetic flux
 The effect is called
mutual inductance
Section 21.4
Transformers
 Transformers make use of mutual inductance to
increase or decrease the amplitude of an applied AC
voltage
 A simple transformer consists of two solenoid coils with
the loops arranged so that all or most of the magnetic
field lines and flux generated by one coil pass through
the other coil
Section 22.9
Transformers, cont.
 The wires are covered with a nonconducting layer so
that current cannot flow directly from one coil to the
other
 An AC current in one coil will induce an AC voltage
across the other coil
 An AC voltage source is typically attached to one of
the coils called the input coil
 The other coil is called the output coil
Transformers, Equations
 Faraday’s Law applies to both coils
 out
 in
Vin 
and Vout 
t
t
 If the input coil has Nin coils and the output coil has
Nout turns, the flux in the coils is related by
Nout
 out 
 in
Nin
 The voltages are related by
Nout
Vout 
Vin
Nin
Section 22.9
Transformers, final
 The ratio of the turns can be greater than or less
than one
 Therefore, the input voltage can be transformed to a
different value
 Transformers cannot change DC voltages
 Since they are based on Faraday’s Law
Section 22.9
Practical Transformers
 Most practical
transformers have central
regions filled with a
magnetic material
 This produces a larger
flux, resulting in a larger
voltage at both the input
and output coils
 The ratio Vout / Vin is not
affected by the presence
of the magnetic material
Section 22.9
Transformers and Power
 The output voltage of a transformer can be made
much larger by arranging the number of coils
 According to the principle of conservation of energy,
the energy delivered through the input coil must
either be stored in the transformer’s magnetic field
or transferred to the output circuit
 Over many cycles, the stored energy is constant
 The power delivered to the input coil must equal the
output power
Section 22.9
Power, cont.
P=VI
 if Vout > Vin, then Iout < Iin
 Pin = Pout only in an ideal transformer
 In real transformers, the coils always have a small
electrical resistance which causes some power
dissipation
 For a real transformer, the output power is always less
than the input power (usually by only a small amount)
 Small current means little power loss to resistance of
power lines
Section 22.9
Applications of Transformers
 Transformers are used in the transmission of electric
power over long distances
 Power dissipation in a electrical wire is P = V I
 DC voltage would waste too much energy in
transmission
 Transformers allow large AC voltage transmission with
small current
 Many household appliances use transformers to
convert the AC voltage at a wall socket to the smaller
DC voltages needed in many devices
Section 22.9
Applications of Induction
 A ground fault interrupter (GFI) is a safety device used in many household
circuits
 It uses Faraday’s Law along with an electromechanical relay
 The relay uses the current through a coil to exert a force on a magnetic
metal bar in a switch
 During normal operation, there is zero magnetic field in the relay
 If the current in the return coil is smaller, a non-zero magnetic field opens the
relay switch and the current turns off
Section 21.7
Electric Guitars
 An electric guitar uses
Faraday’s Law to sense
the motion of the strings
 The string passes near a
pickup coil wound around
a permanent magnet
 As the string vibrates, it
produces a changing
magnetic flux
 The resulting emf is sent
to an amplifier and the
signal can be played
through speakers
Section 21.7
Railgun
 Current produces a large magnetic
field which interacts with the
current to produce a large force on
the projectile
 Projectile speeds much greater
than conventional ballistics are
possible
 Proposed uses are
 Weapons
 Space Program
 Inertial Confinement Fusion
 http://www.youtube.com/watch?v=6BfU-wMwL2U