Transcript Chapter 20 Induced Voltages and Inductance 20.1 Induced emf  A current can be produced by a changing magnetic field [B=f (t)], i.e., B varies over time 

Chapter 20
Induced Voltages and
Inductance
20.1 Induced emf

A current can be produced
by a changing magnetic
field [B=f (t)], i.e., B varies
over time
 First shown in an
experiment by Michael
Faraday
 A primary coil is
connected to a
battery
 A secondary coil is
connected to an
ammeter
Michael Faraday

Faraday is often regarded
as the greatest
experimental scientist of
the 1800s. His contributions
to the study of electricity
include the invention of the
electric motor, generator,
and transformer.
Faraday’s Experiment
The purpose of the secondary circuit is to
detect current that might be produced by the
magnetic field
 When the switch is closed, the ammeter
deflects in one direction and then returns to
zero
 When the switch is opened, the ammeter
deflects in the opposite direction and then
returns to zero
 When there is a steady current in the primary
circuit, the ammeter reads zero

Faraday’s Conclusions
 An
electrical current is produced
by a changing magnetic field
 It is customary to say that an
induced emf is produced in the
secondary circuit by the
changing magnetic field
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 wire loop wire and the
area of the loop

Magnetic Flux, 2
You are given a loop of
wire
 The wire is in an uniform
magnetic field B
 The loop has an area A
 The flux is defined as
 ΦB = BA = B A cos θ
 θ is the angle
between B and the
normal to the plane

Magnetic Flux, 3


(a) When the field is
perpendicular to the plane
of the loop, θ = 0 and ΦB =
ΦB, max = BA
(b) When the field is
parallel to the plane of the
loop, θ = 90° and ΦB = 0


The flux can be negative, for
example if θ = 180°
SI units of flux are T m² =
Wb (Weber)
Magnetic Flux, final

The flux can be visualized with respect to
magnetic field lines

The value of the magnetic flux is proportional to
the total number of lines passing through the loop
When the area is perpendicular to the lines,
the maximum number of lines pass through
the area and the flux is a maximum
 When the area is parallel to the lines, no lines
pass through the area and the flux is 0

20.2 Electromagnetic
Induction




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
Electromagnetic Induction –
Results of the Experiment

A current is set up in the circuit as long
as there is relative motion between the
magnet and the loop


The same experimental results are found
whether the loop moves or the magnet
moves
The current is called an induced current
because it is produced by an induced
emf
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 through each loop changes by
ΔΦ during an interval Δt, the average emf
induced is given by Faraday’s Law:
 B
  N
t
Faraday’s Law and Lenz’ Law
 The
minus sign is included
because of the polarity of the emf.
The induced emf in the coil gives
rise to a current whose magnetic
field OPPOSES ( Lenz’s law)
the change in magnetic flux that
produced it
There are three possibilities to
produce an emf
1) Time-varying magnetic field
=-N[(A cos)(B/t)+
2) Time-varying loop area
+(B cos )(A/t)+
3) Turning of the loop
(generator)
+BA([cos]/t)]
Applications of Faraday’s Law
– Ground Fault Interrupters

The ground fault interrupter (GFI) is a
safety device that protects against
electrical shock
 Wire 1 leads from the wall outlet to
the appliance
 Wire 2 leads from the appliance
back to the wall outlet
 The iron ring confines the magnetic
field, which is generally 0

If a leakage occurs, the field
is no longer 0 and the
induced voltage triggers a
circuit breaker shutting off
the current
Applications of Faraday’s Law
– Electric Guitar
A vibrating string induces
an emf in a 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

Applications of Faraday’s Law
– Apnea Monitor
The coil of wire
attached to the chest
carries an alternating
current
 An induced emf
produced by the varying
field passes through a
pick up coil
 When breathing stops,
the pattern of induced
voltages stabilizes and
external monitors sound
an alert

20.3 Application of Faraday’s
Law – Motional emf



A straight conductor of
length ℓ moves
perpendicularly with
constant velocity through a
uniform field
The electrons in the
conductor experience a
magnetic force
 F = q v B
The electrons tend to
move to the lower end of
the conductor
ℓ
Motional emf
As the negative charges accumulate at the
base, a net positive charge exists at the
upper end of the conductor
 As a result of this charge separation, an
electric field is produced in the conductor
 Charges build up at the ends of the conductor
until the downward magnetic force is
balanced by the upward electric force
 There is a potential difference between the
upper and lower ends of the conductor

Motional emf, cont.
V =Eℓ
F=qvB
F=qE=q (V/ℓ ) =qvB
V=Bℓv, voltage across the conductor
 If
the motion is reversed, the polarity
of the potential difference is also
reversed
Magnitude of the Motional emf
 B  BA  Bx
 B
x
 
 B
 Bv
t
t
Motional emf in a Circuit

A conducting bar sliding
with v along two conducting
rails under the action of an
applied force Fapp. The
magnetic force Fm opposes
the motion, and a
counterclockwise current is
induced.
Motional emf in a Circuit, 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
Example: Operating a light bulb
Rod and rail have negligible resistance but the bulb has a
resistance of 96 W, B=0.80 T, v=5.0 m/s and ℓ =1.6 m.
Calculate (a) emf in the rod, (b) induced current (c) power
delivered to the bulb and (d) the energy used by the bulb in 60 s.
(a) =vBℓ
 =(5.0 m/s)(0.80 T)(1.6 m)=6.4 V
(b) I=/R
I=(6.4V)/(96 W)=0.067 A
(c) P=I
P=I=(6.4 V)(0.067 A)=0.43 W
(d) E=Pt
E=(0.43 W)(60 s)=26 J (=26 Ws)
20.4 Lenz’ Law Revisited –
Moving Bar Example


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
Lenz’ Law, Bar Example, cont
The flux due to the external field is increasing
into the page
 The flux due to the induced current must be
out of the page
 Therefore the current must be
counterclockwise when the bar moves to the
right

Lenz’ Law, Bar Example, final
The bar is moving
toward the left
 The magnetic flux
through the loop is
decreasing with time
 The induced current
must be clockwise to
to produce its own
flux into the page

Lenz’ Law Revisited,
Conservation of Energy
Assume the bar is moving to the right
 Assume the induced current is clockwise





The magnetic force on the bar would be to the
right
The force would cause an acceleration and the
velocity would increase
This would cause the flux to increase and the
current to increase and the velocity to increase…
This would violate Conservation of Energy
and so therefore, the current must be
counterclockwise
Lenz’ Law, Moving Magnet
Example


(a) A bar magnet is moved to the right toward a
stationary loop of wire. As the magnet moves, the
magnetic flux increases with time
(b) The induced current produces a flux to the left to
counteract the increasing external flux to the right
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
Application – Tape Recorder

A magnetic tape
moves past a
recording and
x
playback head
 The tape is a plastic
ribbon coated with
iron oxide or
chromium oxide
Application – Tape Recorder,
cont.


To record, the sound is
converted to an electrical
signal which passes to an
electromagnet that
magnetizes the tape in a
particular pattern
To playback, the
magnetized pattern is
converted back into an
induced current driving a
speaker