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Chapter 20
Induced Voltages and
Inductance
Electromagnetic Induction
Sections 1–4
General
Physics
Michael Faraday
 1791 – 1867
 Great experimental
scientist
 Discovered
electromagnetic induction
 Invented electric motor,
generator and transformer
 Discovered laws of
electrolysis
General
Physics
Faraday’s Experiment
 A current can be induced by a changing magnetic field
 First shown in an experiment by Michael Faraday
– A primary coil is connected to a battery and a secondary coil is
–
–
–
–
connected to an ammeter
When the switch is closed, the ammeter reads a current and
then returns to zero
When the switch is opened,
the ammeter reads a current in
the opposite direction and
then returns to zero
When there is a steady current
in the primary circuit, the
ammeter reads zero
WHY?
General
Physics
Faraday’s Startling Conclusion
 An electrical current in the primary coil creates a magnetic field
which travels from the primary coil through the iron core to the
windings of the secondary coil
 When the primary current varies (by closing/opening the switch),
the magnetic field through the secondary coil also varies
 An electrical current is induced
in the secondary coil by this
changing magnetic field
 The secondary circuit acts as if a
source of emf were connected to
it for a short time
 It is customary to say that an
induced emf is produced in the
secondary circuit by the
changing magnetic field
General
Physics
Magnetic Flux
 The emf is actually induced by a change in the
quantity called the magnetic flux rather than
simply by a change in the magnetic field
 Magnetic flux is defined in a manner similar to
that of electrical flux
 Magnetic flux is proportional to both the strength
of the magnetic field passing through the plane of
a loop of wire and the area of the loop
General
Physics
Magnetic Flux, cont
 Consider a loop of wire with area A in a uniform magnetic field B
 The magnetic flux through the loop is defined as
 B  B A  BA cos
where θ is the angle between B and the normal to the plane
 SI units of flux are T. m² = Wb (Weber)
Active Figure: Magnetic Flux
General
Physics
Magnetic Flux, cont
 The value of the magnetic flux is
proportional to the total number of
lines passing through the loop
 When the field is perpendicular to the
plane of the loop (maximum number of
lines pass through the area), θ = 0 and
ΦB = ΦB, max = BA
 When the field is parallel to the plane of
the loop (no lines pass through the
area), θ = 90° and ΦB = 0
 Note: the flux can be negative, for
example if θ = 180°
General
Physics
Electromagnetic Induction –
An Experiment
 When a magnet moves toward a loop
of wire, the ammeter shows the
presence of a current (a)
 When the magnet is held stationary,
there is no current (b)
 When the magnet moves away from
the loop, the ammeter shows a current
in the opposite direction (c)
 If the loop is moved instead of the
magnet, a current is also detected in a
similar manner
 An induced emf is set up in the circuit
as long as there is relative motion
between the magnet and the loop
Active Figure: Induced Currents
General
Physics
Faraday’s Law and
Electromagnetic Induction
 The instantaneous emf induced in a circuit
equals the time rate of change of magnetic
flux through the circuit
 If a circuit contains N tightly wound loops
and the flux changes by ΔΦB during a time
interval Δt, the average emf induced is given
by Faraday’s Law:
B
  N
t
General
Physics
Faraday’s Law and Lenz’ Law
 The change in the flux, ΔΦB, can be produced by a
change in B, A or θ
– Since ΦB = B A cos θ
 The negative sign in Faraday’s Law is included to
indicate the polarity of the induced emf, which is
found by Lenz’ Law
– The current caused by the induced emf travels in the
direction that creates a magnetic field whose flux opposes
the change in the original flux through the circuit
General
Physics
Lenz’ Law – Example 1
 Consider an increasing magnetic
field B through the loop
 The magnetic field becomes
larger with time
– magnetic flux increases
 The induced current I will
produce an induced field B ind in
the opposite direction which
opposes the increase in the
original magnetic field
General
Physics
Lenz’ Law – Example 2
 Consider a decreasing magnetic
field B through the loop
 The magnetic field becomes
smaller with time
– magnetic flux decreases
 The induced current I will
produce an induced field B ind in
the same direction which
opposes the decrease in the
original magnetic field
General
Physics
Applications of Faraday’s
Law – Electric Guitar
 A vibrating string induces an
emf in a pickup coil
 A permanent magnet inside
the coil magnetizes a portion
of the string nearest the coil
 As the string vibrates at some
frequency, its magnetized
segment produces a changing
flux through the pickup coil
 The changing flux produces
an induced emf that is fed to
an amplifier

B
 
 A
t
t
General
Physics
Applications of Faraday’s Law
– Transformer
 A varying voltage is applied to
the primary coil
 This causes a varying current
in the primary coil which
creates a changing magnetic
field which travels from the
primary coil through the iron
core to the windings of the
secondary coil
 An electrical current is induced
in the secondary coil by this
changing magnetic field
 The secondary circuit acts as if
a voltage were connected to it
N2
V2 
V1
N1
General
Physics
Application of Faraday’s Law
– Motional emf
 A complete electrical circuit is
fashioned by a rectangular loop
composed of a conductor bar, two
conductor rails, and a load
resistance R.
 As the bar moves to the right with
a given velocity, the free charges
in the conductor experience a
magnetic force along the length of
the bar
 This force sets up an induced
current because the charges are
free to move in the closed path of
the electrical circuit
General
Physics
Motional emf, cont
 As the bar moves to the right, the
area of the loop increases by a
factor of Δx during a time
interval Δt
 This causes the magnetic flux
through the loop to increase with
time
 An emf is therefore induced in
the loop given by

A
x
 
 B
  B
  Bv
t
t
t
General
Physics
Motional emf, cont
 The changing magnetic flux
through the loop and the
corresponding induced emf in the
bar result from the change in
area of the loop
 The induced, motional emf, acts
like a battery in the circuit

B v
  B v and I 
R
B v
B vLaw,
and
The induced current, by 
Ohm’s
is I 
R
Active Figure: Motional emf
General
Physics
Lenz’ Law Revisited – Moving
Bar Example 1
 As the bar moves to the right,
the magnetic flux through the
circuit increases with time
because the area of the loop
increases
 The induced current must be
in a direction such that it
opposes the change in the
external magnetic flux
 The induced current must be
counterclockwise to produce
its own flux out of the page
which opposes the increase in
the original magnetic flux
General
Physics
Lenz’ Law Revisited – Moving
Bar Example 2
 The bar is moving toward
the left
 The magnetic flux through
the loop decreases with time
because the area of the loop
decreases
 The induced current must be
clockwise to produce its own
flux into the page which
opposes the decrease in the
original magnetic flux
General
Physics
Lenz’ Law Revisited – Moving
Magnet Example 1
 A bar magnet is moved to the
right toward a stationary loop of
wire
– As the magnet moves, the
magnetic flux increases with time
 The induced current produces a
flux to the left which opposes
the increase in the original flux,
so the current is in the direction
shown
General
Physics
Lenz’ Law Revisited – Moving
Magnet Example 2
 A bar magnet is moved to the
left away from a stationary loop
of wire
– As the magnet moves, the
magnetic flux decreases with time
 The induced current produces
an flux to the right which
opposes the decrease in the
original flux, so the current is in
the direction shown
General
Physics
Lenz’ Law, Final Note
 When applying Lenz’ Law, there are two
magnetic fields to consider
– The external changing magnetic field that
induces the current in the loop
– The magnetic field produced by the current in
the loop
General
Physics