PHY
2054C
– College
B
Electricity,
Magnetism,
Light, Optics Physics
and Modern Physics
L6—Ch21
spring 2013
WÜA Wtä|w `A _|Çw
magnetic induction
Chapter 21
Today’s Lecture: purpose & goals
1) Induced Voltage
(Faraday’s Law),
2) Lenz's Law
3) Generators and
Transformersq,vF
FN
Fs
q,v
F
R
B
Torque on a Coil due to
Magnetic Field
Current loop “coil” on the right;

Left and Right wire have different
current directions;
RHR-> F1 into page, F I l B sin
F2 out of page F
I a B, F I a B


1
2
b
F 1 sin
2
I a b B sin

b
F 2 sin
2
If the coil has N windings, and area A=ab
N I A B sin
between
coil face and B
Result: simple DC motor


A coil is pivoted to rotate freely inside a magnetic
field.  current thru coil, causes a torque.
When the coil has turned by 90°, switch current
direction, so that it continues to turn (commutator)
Hur sluta röka cold turkey
q,v
Very Simple Motors
….including Michael Faraday’s
first demonstration of motion
induced by the flow of current
wire
…feels a force!
outward
I
B
Strong magnet
Important Points
from last Lecture

“First” RightHand Rule
1) Magnetic Fields are generated by
moving charges, currents

straight wire:
B

2
I
,
r
0
4
q v B sin
Force on current
F
7
T m
A
N
I
0
l
2) Effect of Magnetic Field;
Force on moving charges
F

10
current in long coil:
B

0
I l B sin
Torque on coil area A
“Second” RightHand Rule
N I A B sin
Intro: Induced Voltage



Michael Faraday thought: “If current produces a magnetic
field, why can't a magnetic field produce a current?”
When switch is closed, coil X builds up a magnetic field in
magnet core
 Galvanometer shows negative current through coil Y
When switch is opened, the magnetic field disappears,
 and a positive current is shown
[Notice that the effect is transient; it only happens for a short time
right after the opening or closing]
Intro: Induced Voltage
“Faraday’s Law”
 Inserting a magnet into
a coil also produces
an induced voltage (ind)
or current.
 ind
N
t
 [the key here is change!!]
 The faster speed of
insertion/retraction, the higher the induced
voltage.
 What we change here is called the “magnetic
flux”, the amount of field B that passes through
an area A:
B A cos
Magnetic Flux, cont.




If the field is perpendicular to the surface, B = B A
If the field makes an angle θ with the normal to the
surface, B = B A cosθ
If the field is parallel to the surface, B = 0
“How strong the magnetic field is in that region of space”
Section 21.2
Faraday’s Law, Summary


Only changes in the magnetic flux matter
Rapid changes in the flux produce larger values of emf
than do slow changes


The magnitude of the emf is proportional to the rate
of change of the flux
 If the rate is constant, then the emf is constant


This dependency on frequency means the induced emf
plays an important role in AC circuits
In most cases, this isn’t possible and AC currents result
The induced emf is present even if there is no current
in the path enclosing an area of changing magnetic
flux
ind
changing

BAcos
ind
N t
V
 =IR
ind
ind
B
0
N
I
l
Section 21.2
Lenz's Law



Sometimes it is hard to figure out the sign of the induced
voltage; There is a simple rule:
A change in flux gives rise to an induced current
whose magnetic field always opposes the
original change.
(No formula) – this is the minus sign  ind
N
t
in Faraday’s law
At the time of closing the switch
B2
Primary current
 ind
ind
N t
ΔB1
V
Induced Current
ind
 =IR
Opposite directions!!
B
ind
N
I
0
l
Lenz's Law2 and Example
“Eddy Currents”



“Induced current opposes the
change that caused it”
dropping a strong magnet
through a copper tube:
Induced Current
S
Induced currents - B above
act attractively
N


Induced current's - B below
magnet act repulsively
Magnet will fall, but very slowly!
Induced Current
Question 1




ew
vi
e
R
If we send the same magnet through a pipe with a
slit along the side, we would expect the magnet to
a) fall at the same, slow rate as in the solid pipe
b) fall even slower
c) fall much faster
Lenz's Law



Sometimes it is hard to figure out the sign of the induced
voltage; There is a simple rule:
A change in flux gives rise to an induced current
whose magnetic field always opposes the
original change.
(No formula) – this is the minus sign  ind
N
t
in Faraday’s law
At the time of closing the switch
B2
Primary current
 ind
ind
N t
V
ΔB1
Induced Current
ind
 =IR
Opposite directions!!
B
N
I
0
l
ind
Question 1








When do you expect to see the
lightbulb turn on?
lightbulb
a) when it’s at the top
b) when it’s at the bottom
c) on one side or the other
solenoid coil
pole face of
magnet
Anything special about the lightbulb flash?
a) it turns on a very short time
b) it turns on twice per revolution
c) it stays on for most of the revolutuion
Lenz’ Law

Lenz's Law: An induced emf gives rise to a current
whose magnetic field opposes the original change in
magnetic flux.
Magnetic Flux is reduced,
 Induced current
tries to add to Flux
Magnetic Flux is increased,
 Induced current
tries to reduce Flux
The direction of the induced current comes from
“right-hand rule”1: fingers: curled B, thumb: I:
Problem Solving with

Lenz’s Law
Lenz's Law: An induced emf gives rise to a A
current
cos in
whose magnetic field opposes the originalBchange
magnetic flux.
B A cos
ind

Four steps:
indof theNMagnetic Flux?
 What is the direction
t
N
t
[Out of North magnetic pole, into South magnetic pole.]



Is the flux through the loop increasing or decreasing?
Apply Lenz’s Law
 if increasing, induced field will be in opposite
direction of original field.
 if decreasing, induced field will be in same
direction as original field.
I
What direction will current be
flowing around loop?
B
 Use 1st RHR
(out)
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
Reading computer memory


Magnetic read-heads on computer harddrives and magnetic cassette tapes sense
information stored in magnetic domains
this same way!!
The voltage generated in the pickup coil
is caused by the changing magnetic
flux at the boundaries between north
and south-facing magnetic domains
Section 21.7
Bicycle Odometers

An odometer control unit is shown,



which receives signals from a pickup coil mounted on the axle support
A permanent magnet is attached to a wheel that passes the coil with
each wheel revolution.
When the magnet passes over the pickup coil, it changes the
magnetic flux thru the coil, and a pulse is generated

A computer keep tracks of the number of pulses
Road Traffic Sensors works similarly:



a pickup coil is buried in the roadway
When the ferrous parts of a car (or
currents from the car’s electrical circuits)
pass over the coil, a pulse is generated
that records the arrival of the car ; only moving cars sensed!!
Section 21.7
Faraday's Law of Induction

The induced Voltage (emf ε) in a coil is winding number N
times the change of the magnetic flux  through the coil per
time;
 ind

N
t
where the magnetic flux is defined as the magnetic field
B passing through a loop of area A
B A cos

The angle θ is measured between the
normal direction of the area and
the magnetic field direction
Changing the Flux
B A cos
ind





N
t
The magnetic flux  is given by a
product of B, A and cos(θ).
Therefore there are three ways of creating a change in
flux and therefore an induced emf.
a) changing A
b) changing B
c) changing cos(θ)
Changing cos(θ)
B Acos


Turning a coil in a
magnetic field:
Only cos(θ) changes
ind
ind

B A cos
t
cos
NBA
t
NBA
0
N
this induces an AC voltage
in the coil.
Electric Generator




Electric Generator:
A permanent (or electro)magnet (rotor) with many
poles is rotating through
many loops of wire.
The rotation keeps
changing the flux
through each of the
stationary (stator) coils,
which induces voltage on
the output.
 When we use the voltage by drawing a current, the
magnetic field of the induced current acts like a brake!
(it’s removing energy!!)
Motor-Generator


An electric motor sends a
current through a coil in a
magnetic field, which starts
to turn.
Electrical  Mechanical
energy
energy
 A generator turns a coil in
a magnetic field, which
produces current.
 Mechanical  Electrical
energy
energy
Every motor is a generator  and vice versa
Question 2





A generator, which is being turned by a hand-crank
is hooked up with a switch to a light bulb.
When the switch is closed, the cranking of the
generator
a) gets harder
b) does not change
c) gets easier
Transformers


Transformers are devices that can 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
Changing B

B Acos
Primary winding uses AC current and
voltage

secondary winding produces AC
current and voltage
What are the voltages?
,V P N P
t
VS NS
VP NP
 What are the currents ?
B NS I S , B NP I P
B
B
t
IS
IP
Voltage
VS NS
B
NP
NS
primary
secondary
Current

primary
 The electric power is the same in and out!
NS
NP
secondary
VP
I = V P I P = PP
PS = V S I S
NP
NS P
 This assembly is called a transformer.
 It allows us to change voltages of AC without losing power!
Question
The primary winding of an electric train transformer has
400 turns, and the secondary has 50. If the input voltage
is 120 V(rms), what is the output voltage?
1.
2.
3.
4.
480 V
60 V
15 V
10 V
Changing B
B Acos
Primary winding uses AC current and

voltage
secondary winding produces AC

current and voltage
What are the voltages?
B
B
,V P N P
t
t
VS NS
VP NP
 What are the currents ?
IS
B NS I S , B NP I P
IP
 somewhat idealized:
Voltage
VS NS
B
primary
secondary
NP
NS
Current

primary
 (the total magnetic flux thru the primary
coils doesn’t all pass thru the secondary):
 efficiency e (fraction of flux actually transferred)
 real transformers:
IS
IP
e
NP
NS
secondary
VS
VP
e
NS
NP
Stay tuned. . . .


Wednesday: problem solving (Chs. 21): Magnetism
and Induction
Friday: Chapter 22 Electromagnetic Waves
http://www.physics.fsu.edu/courses/summer2010/phy2054
c
How do you like my
magnetic
personality!!
Another Faraday Experiment




A solenoid is positioned near a loop of wire with the lightbulb
He passed a current through the solenoid by connecting it to a
battery
When the current through the solenoid is constant, there is no
current in the wire
When the switch is opened or closed, the bulb does light up
Section 21.1