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This Week
Magnetism: Are you attracted or repulsed?
Where does magnetism come from?
What use is magnetism?
Post pictures and notes on refrigerators
Electrical motors turn electricity into work
Generators turn heat energy into electricity
Transformers for power transmission and Ipod.
Earths Magnetic field. Northern lights.
5/8/2017
Physics 214 Fall 2011
1
Magnetism
Electric charge is also responsible for the force that
we call magnetism.
Moving charge, that is a current, produces a force
field which we term the magnetic field B.
Since atoms contain “moving charge” most atoms
and substances have magnetic behavior. In the case
of iron this effect is very strong.
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Magnetic field
There are differences between the
electric field and the magnetic field.
 A magnet has two poles and a
magnetic monopole has never been
observed.
The field lines are continuous loops
Like poles repel and unlike poles
attract
A magnetic field only acts on moving
charge
The force is perpendicular to the
velocity so the moving charge is
accelerated but does not gain or lose
energy
By definition the field
lines enter a south
pole and leave a
north pole
http://www.physics.purdue.edu/class/applets/phe/mfbar.htm
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Earth’s magnetic field
The earth has a dipole field
inclined at 11 degrees to the axis
of rotation.
The North Pole (Arctic) is
actually a magnetic south pole.
It is thought that the field is
produced by circulating electric
currents in the molten iron core.
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Form of the force
The force a charged particle moving with
velocity v in a magnetic field B is given
by
or
F = qvperpendicularB
F = qvBperpendicular
This means the maximum force is when v
is at right angles to B and that the force
is zero if v is parallel to B or v = 0.
For a current in a wire qv = qL/t = IL so
the force on a current carrying wire of
length L is
F = ILBperp
Units of B are tesla
(N x sec/coulombs x meters)
(N/amps.meters)
http://www.physics.purdue.edu/class/applets/phe/lorentzforce.htm
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Fields from currents
A current carrying wire produces
circular field lines. Looking along
the direction of the current the field
lines are clockwise
http://www.physics.purdue.edu/class/applets/phe/mfwire.htm
A current loop produces a dipole
field
A solenoid can produce a strong
uniform field in a volume with small
leakage. If it is placed in an iron
cylinder the field is stronger and
more contained
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Force between two infinite wires
If the two wires are very long
then each wire sits in a B
field which is at right angles
to the wire.
F/L = 2k’ I1 I2 /r
k’ = 1 x 10-7N/amp2
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Force on a coil: Meters and Motors
http://www.physics.purdue.edu/class/applets/phe/electricmotor.htm
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Moving conductorB
Suppose a wire is moving with
velocity v in a magnetic field so that
v is into the screen.
Positive charge will feel a force to the
right.
If the wire is isolated then an
electromotive force will exist
between the ends of the wire and if
the wire is part of a circuit this
electromotive force will cause a
current to flow.
The electrical energy is produced by
the force that is moving the wire and
the wire requires a force to keep it
moving at constant velocity
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Physics 214 Fall 2011
F
ε
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Induction
If a conductor is in a changing magnetic
field an electromotive force is produced.
If the conductor is part of a circuit then a
current will flow.
The induced current produces it’s own
magnetic field and the direction of the
induced current produces a magnetic field
that opposes the change.
Self induction occurs when the current
changes in a circuit for example when it is
switched on or disconnected. The induced
EMF slows down the change of current.
anim0018.mov
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Physics 214 Fall 2011
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Magnetic flux
In order to determine the induced EMF we
have to define how the magnetic field
changes as we move a conductor through a
magnetic field.
The important quantity is called magnetic flux
and it is a product of the magnetic field
perpendicular to the loop times the area
Ф = BperpendicularA
If we have a loop of N turns
B
ε = NΔФ/t
So if we turn 50 loops in 1/20 second
ε = ΔФ/t
= 1000BA
so if B was 1/10 tesla and A = 1/100
Ф= BA
m2
0
-BA
Rotating a coil
ε = 1 volt
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Transformers and generators
The changing current in the primary produces
changing magnetic flux in the secondary and an
induced voltage.
AC
AC
Ф
Naturally generates AC
Ф
ΔV2/ ΔV1 = N2/N1 can be
step up or step down
http://www.physics.purdue.edu/class/applets/phe/generator_e.htm
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Summary of Chapter 14
Current produces a magnetic force field
F = qvperpB moving charge
F = ILBperp current
Torque on a current loop - meters and motors
F/L = 2k’ I1 I2 /r
k’ = 1 x 10-7N/amp2
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Induction
Ф = BperpendicularA
ε = NΔФ/t
Transformer
ΔV2/ ΔV1 = N2/N1
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Generator
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Magnetic field of the earth
Liquid metal moving through a
magnetic field generates a current,
similar to that induced in the
moving coil of an electric
generator. That current in turn
generates the magnetic field. This
"self-generation" mechanism can
dramatically amplify the small,
random fields that always exist in
magnetic materials. To do this,
though, the flow must be both
complex, mixing up the
longitudinal and latitudinal
directions, and rapid, "tangling up"
magnetic field lines faster than
they can untangle.
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When filled with molten sodium
and stirred at up to 26 revolutions
per second, this tank generates a
magnetic field--similar to the way
the Earth's core creates a field.
Previous experiments controlled
the flow more carefully and
avoided turbulence, so they were
less like the Earth's core.
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Earth’s magnetic field
On Earth, the record of the reversal of
the magnetic field is preserved in
magnetic rocks which lie along the
ocean floor.
The magnetism preserved in these
rocks points first in one direction, then
in another direction.
These rocks are lava flows or layers of
microscopic sea creatures. The
average time between reversals is ~
250,000 years.
The field traps charged particles in
areas called the Van Allen belts. The
field protects us from charged particles
except at the poles
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6A-02 Weighing a Suspended Magnet
Using equal and opposite forces between magnets to weigh magnet
Will the
scale still
balance
when the
second
magnet
floats ?
Fmagnetic
Fgravity
Fgravity
Fmagnetic
?
The scale will
read the sum of
forces acting on
bottom magnet:
Fmagnetic + Fgravity
The top magnet
is floating so:
Fmagnetic = Fgravity
The scale reads:
Fmagnetic + Fgravity =
2 Fgravity = 2mg
THE SECOND MAGNET’S WEIGHT IS SENSED BY
THE BALANCE EVEN THOUGH IT ISN’T ACTUALLY
“TOUCHING” THE APPARATUS.
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6B-02 Force on a Moving Charge
Which
orientation of the
magnet causes
the beam to
move upward ?
Downward ?
Force
Investigating the behavior of moving charge in magnetic field
F = q (v┴ B)
MAGNETIC FIELD CAUSES THE CHARGED
PARTICLES TO DEFLECT. WE FIND THE DIRECTION
OF FORCE WITH THE RIGHT-HAND RULE. THIS IS
THE FORCE ON POSITIVE CHARGE!
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6B-06 Magnetic Force on a Current-Carrying Conductor
Finding the direction of Force on Current due to B-field
Based on the
direction of the
Magnetic Field and
the direction that
current flows, can
you predict in which
direction the Force
points ?
F/L = I┴ B
B
F
I┴
Use right-hand rule to find direction of F
CURRENT FLOWING ALONG THE AXLE IS PERPENDICULAR
TO THE MAGNETIC FIELD. THERE IS A FORCE ON THE AXLE,
CAUSING IT TO ROLL. IF THE CURRENT IS REVERSED, THE
AXLE ROLLS IN THE OPPOSITE DIRECTION.
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6B-11 Force Between Coil and Wire
Forces between two conductors
What occurs when
the current is sent
through? How
about reversing the
current ?
What differences
occur in the
interacting fields if
one of the wires is
replaced by a
solenoid ?
WHEN THE SOLENOID IS ACTIVATED AND A CURRENT IS SENT
THROUGH THE WIRE, THE WIRE WRAPS ITSELF AROUND THE
SOLENOID. WHEN THE CURRENT IN THE WIRE IS REVERSED, IT
WRAPS AROUND THE SOLENOID IN THE OPPOSITE DIRECTION.
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6D-11 Jumping Ring
Is there any
differences in
the two rings ?
Why one can
jump up, the
other can’t ?
INDUCED CURRENT IN THE RING, CAUSED BY THE GROWING
MAGNETIC FIELD WHEN THE SWITCH IS ACTIVATED, IS
RESPONSIBLE FOR THE REPULSIVE FORCE BETWEEN THE COIL
AND THE RING. IF A SPLIT RING IS PLACED OVER THE
ELECTROMAGNET, THE COIL WILL NOT JUMP BECAUSE OF THE
BROKEN “CIRCUIT” IN THE RING, PREVENTING THE CURRENT FLOW.
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Questions Chapter 14
Q1 The north pole of a hand-held bar magnet is brought near the
north pole of a second bar magnet lying on a table. How will the
second magnet tend to move?
It will be repelled
Q4 Is it possible for bar magnet to have just one pole?
The magnetic fields produced by currents require both a north
and south poles. These poles do not exist as physical entities like
an electron with one unit of charge. Physical laws do not prohibit
the existence of monopoles, that is particles with “magnetic
charge”, these have been searched for but never observed.
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Q6 If we regard the earth as magnet, does its magnetic north pole
coincide with its geographical north pole? What defines the
position of the geographical north pole?
The geographical north pole is defined by the axis of rotation. The
magnetic north pole is determined by the currents and fields in the
iron core of the earth. About every 250,000 years the field of the
earth reverese.
Q7 We visualized the magnetic field of the earth by imagining that
there is a bar magnet inside the earth (fig. 14.7). Why did we draw
this magnet with its south pole pointing north?
The definition of the North pole is the point at which the North pole
of a magnet would point. This means the North pole is a physical
magnetic south pole.
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Q9 A horizontal wire is oriented along an east-west line, and a
compass is placed above it. Will the needle of the compass deflect
when a current flows through the wire from east to west, and if so,
in what direction?
The current will produce a field that appears clockwise looking
west. This means the compass will point north/south
Q11 A uniform magnetic field is directed horizontally toward the
north, and a positive charge is moving west through this field. Is
there a magnetic force on this charge, and if so, in what
direction?
Point index finger along the velocity, the middle finger in the
direction of B and then the thumb points in the direction of the
force. The force points up.
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Q12 A positively charged particle is momentarily at rest in a
uniform magnetic field. Is there a magnetic force acting on this
particle?
No. The particle must have a velocity.
Q13 If a uniform magnetic field is directed horizontally toward the
east, and a negative charge is moving east through this field, is there
a magnetic force on this charge, and if so, in what direction?
No. There must be an angle between the velocity and the direction of B
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Q15 If we look down at the top of a circular loop of wire whose plane
is horizontal and that carries a current in the clockwise direction,
what is the direction of the magnetic field at the center of the circle?
The field is perpendicular to the plane in the direction that if you
look in that direction the current is clockwise. So the answer is
down.
Q17 A current-carrying rectangular loop of wire is placed in an
external magnetic field with the directions of the current and field
as shown in the diagram. In what direction will this loop tend to
rotate as a result of the magnetic torque exerted on it?
B
F
B
F
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Q24 A horizontal loop of wire has a magnetic field passing upward
through the plane of the loop. If this magnetic field increases with
time, is the direction of the induced current clockwise or
counterclockwise (viewed from above) as predicted by Lenz’s law?
The current induced produces a magnetic field that opposes the
increase so the induced magnetic field points down so the current
must be clockwise viewed from above.
Q25 Two coils of wire are identical except that coil A has twice as
many turns of wire as coil B. If a magnetic field increases with time at
the same rate through both coils, which coil (if either) has the larger
induced voltage?
The flux in A is twice that in B so the induced voltage is twice as large.
Q28 Does a simple generator produce a steady direct current?
No. As the coil turns at constant angular velocity the rate of
change of flux depends on the angle of the coil to the field so the
current is AC
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Q30 Can a transformer be used, as shown in the diagram below, to
step up voltage of a battery? Explain.
V2/V1 = N2/N1
So if N2 > N1 the voltage
is stepped up.
Q31 By stepping up the voltage of an alternating current source
using a transformer, can we increase the amount of electrical
energy drawn from the source?
No. For an ideal transformer the input power = output power.
In a real transformer energy is lost due to heat. Feel the
transformer for your laptop.
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Ch 14 E 4
Two parallel lines, each carrying I = 2amps, exert a
force per unit length of 1.6 x 10-5 N/m on each other.
What is distance between the lines?
I = 2A
F/ℓ = (2k’ I1I2)/r
r = (2k’ I1I2)/(F/ℓ)
= (2(1 x 10-7)(2)(2))/(1.6 x 10-5)
= 0.05 m
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I
I
r
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Ch 14 E 8
Magnetic force on 40 cm straight wire segment
carrying I = 5A is 2.5N. What is magnitude of magnetic
field perpendicular to wire?
F = IℓB
B = F/Iℓ = (2.5)/(5)(0.40)
= 1.25 T
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B
Physics 214 Fall 2011
I = 5A
0.40m
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Ch 14 E 10
Loop of wire enclosing Area, A = 0.03m2, has magnetic
field passing thru its plane at an angle. Component of
magnetic field perpendicular to plane = 0.4T, while
component parallel to plane = 0.6T. What is magnetic
flux thru coil?
I = B1A = 0.4(0.03)
A
= 0.012Tm2
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Ch 14 E 12
Coil of wire with 60 turns and cross-sectional area, A
= 0.02m2, lies with it’s plane perpendicular to B =
1.5T magnetic field. Coil is rapidly removed B-field in
time t=0.2s.
a) What is initial magnetic flux thru coil?
b) What is average voltage induced in coil?
a)
Φ = NB1A = (60)(1.5)(0.02) = 1.8Tm2
b)
ε
5/8/2017
= ΔΦ/t = (1.8 Tm2 – 0)/0.2s = 9V
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Ch 14 CP 2
Small metal ball has charge q = +0.05C and mass,
m = 0.025kg. Ball enters a region of magnetic field
B = 0.5 T that is perpendicular to its velocity
v = 200m/s.
a) What is magnitude of magnetic force on ball?
b) What is direction of magnetic force on ball?
c) Will this force change magnitude of ball’s velocity?
d) Use Newton’s 2nd Law, what is magnitude of
acceleration of the ball?
e) Centripetal acceleration = v2/r. What is radius of the
curve ball will move thru in magnetic field?
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Ch 14 CP 2 (cont)
ẑ
v  vyˆ
x̂
. .
. .
. .
. .
B  Bxˆ
ŷ
a) F = qv1B = (0.05)(200)(0.5) = 5N
b) (see diagram) Force in –z direction
c) To change magnitude of velocity is to change kinetic energy. If
magnetic field changes kinetic energy then it must do work on charged
ball. The right-hand rule shows us that velocity and force are always
perpendicular. Therefore, the magnetic field can do no work!
d) F = ma = qv1B = 5N
a = 5N/0.025kg = 200 m/s2
e) v2/r = 200m/s2 , r = v2/(200m/s2) = (200m/s)2/200m/s2 = 200m
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Ch 14 CP 4
Transformer is designed to step down line voltage of
110V to 22V. Primary coil has 400 turns of wire.
a) How many turns of wire on secondary coil?
b) Current in primary I1 = 5A. What is max current in
second coil?
c) If transformer gets warm during operation, will current
in secondary coil equal that computed in previous
question (b)?
a) ΔV2/ ΔV1 = N2/N1 , N2 = N1(ΔV2/ ΔV1) = 400(22/110) = 80 turns
b) ΔV2I2 ≤ ΔV1I1
I1 = 110/22 (5) = 25A
Max current in second coil = 25A.
c) No, heat that warms up transformer is power dissipated in the form
P = I2R. Power is lost to heat.
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Waves
In our everyday life there are many examples
of waves for example, Sound, ocean waves,
strings of musical instruments, organ pipes…
These are examples of waves which need a
medium to travel through and the general
definition of such waves is
A disturbance which propagates through a
medium but the medium itself only moves
locally as the wave passes.
A special case of a wave is an
electromagnetic wave which can propagate
through vacuum, e.g. radio, light, x rays ….
Waves transport energy and momentum and
energy is required to generate waves
The medium must have elastic properties
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Wave properties
There are two types of waves
Longitudinal – consists of the
propagation of a series of
compressions and rarefactions and
the local movement of the medium
is an oscillation back and forward
along the direction of the wave
Sound is one example
Transverse – where the movement
of the medium is at right angles to
the velocity of the wave. The strings
of musical instruments is an
example.
5/8/2017
Physics 214 Fall 2011
anim0019.mov
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Periodic waves
One can propagate waves which are a single complicated
pulse e.g. an explosion or a complicated continuous wave
e.g. the wind. We will focus on regular repetitive waves
λ
These waves have a pattern which repeats and the length of
one pattern is called the wavelength λ
The number of patterns which pass a point/second is called
the frequency f and if the time for one pattern to pass is T
then f = 1/T
v = λ/T = fλ
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Waves on a string
If we shake the end of a
rope we can send a wave
along the rope. The rope
must be under tension in
order for the wave to
propagate
v = √(F/μ)
F = TENSION
μ = MASS/UNIT LENGTH
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Standing waves
If two identical waves exist on the
same string but traveling in opposite
directions the result can be standing
waves in which some points never
have a deflection.
These are called nodes and some
points oscillate between plus and
minus the maximum amplitude, these
are called antinodes.
Standing waves provide the notes on
musical instruments. When a string
is secured at both ends and plucked
or hit the generated waves will travel
along the string and be reflected and
set up standing waves.
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