magnetic fields
TRANSCRIPT
AP Physics Rapid Learning Series - 17
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 1
Rapid Learning CenterChemistry :: Biology :: Physics :: Math
Rapid Learning Center Presents …Rapid Learning Center Presents …
Teach Yourself AP Physics in 24 Hours
1/56 *AP is a registered trademark of the College Board, which does not endorse, nor is affiliated in any way with the Rapid Learning courses.
M ti Fi ldMagnetic Fields
Physics Rapid Learning Series
Rapid Learning Centerwww.RapidLearningCenter.com/© Rapid Learning Inc. All rights reserved.
Wayne Huang, Ph.D.Keith Duda, M.Ed.
Peddi Prasad, Ph.D.Gary Zhou, Ph.D.
Michelle Wedemeyer, Ph.D.Sarah Hedges, Ph.D.
AP Physics Rapid Learning Series - 17
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 2
Learning Objectives
By completing this tutorial, you will:
Understand the nature of magnetism.
Examine the relationship between magnetism, force and moving charge.
S l f
3/56
See examples of magnetism in nature and technology.
Concept MapPhysics
Studies
Previous content
New content
Electrical Forces
Electric Charge
Magnetic Forces
When moving
Created from
and
Atoms
4/56
Magnetic Fields
When moving in
Magnetic Domains
Arranged in
Described by
Right Hand Rule
AP Physics Rapid Learning Series - 17
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 3
The Nature of Magnetism
This section will describe the basic nature of magnetism
5/56
nature of magnetism.
Magnetic Domains
The motion of electrons may produce unusual forces. These often cancel out and don’t amount to anything interesting.
In certain materials, groups of atoms have their electrons aligned into small areas called magnetic domains that behave as small magnets themselves.
6/56
AP Physics Rapid Learning Series - 17
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 4
Magnetic Elements
Iron, cobalt, and nickel are common magnetic materials.
These materials are called ferromagnetic.
All materials are magnetic, but most are only VERY slightly magnetic.
7/56
Polarization
The poles of a magnet cannot be separated. There are no magnetic monopoles, unlike electric chargescharges.
8/56
A North pole will always be accompanied by a South pole.
AP Physics Rapid Learning Series - 17
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 5
Attraction and Repulsion
Just like electric charges (poles): likes repel, opposites attract.
S N
S N
N S
N S
9/56
N S N S
Breaking Magnets
If you break a magnet, you don’t get an isolated N and S pole. Each segment becomes its own complete mini magnet.complete mini magnet.
N S
N S One magnet
Two complete magnetsNS
10/56
N SNS
Four complete magnetsNS NS
AP Physics Rapid Learning Series - 17
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 6
Earth as a MagnetThe Earth is a large magnet. Magnetic north and geographic north are not in the same location. The difference between these is called magnetic declinationdeclination.
11/56
Note that what we call the North pole is actually the magnetic south pole of our Earth!
Magnetic Fields
Magnetic fields, B fields, may be drawn similarly to E fields. Go from N to S. E field was + to -.
N S
12/56
Where the lines are more concentrated is an area of higher magnetic flux/strength.
AP Physics Rapid Learning Series - 17
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 7
Field Lines
N S
13/56
A small compass could be used to “trace” the magnetic field lines in simple situations.
N S
Repeatedly moving the compass creates the same field lines as seen before.
Electricity and MagnetismA wire carrying an electric current produces magnetism.
In fact, any moving charge creates magnetism.
14/56
AP Physics Rapid Learning Series - 17
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 8
Earth’s Magnetic Field
This is why the Earth has a magnetic field.
( )The molten metal (charge) in its center is continually rotating.
Thus, a magnetic field is formed around the Earth. This is called the dynamo effect.
15/56
Curious fact: Every few million years, the earth’s magnetic field reverses itself!!!
Other Magnetic Fields
Jupiter spins very fast, this may explain why it has a very large magnetic field.
Most moons in the solar system have no molten core. Thus they have no magnetic field.
16/56
y g
AP Physics Rapid Learning Series - 17
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 9
Moving ChargeMoving Charge, Magnetism, and Force
This section will describe the relationship between magnetic fields moving charge
17/56
between magnetic fields, moving charge, and force.
Right Hand RuleTo visualize magnetic fields and current, use the right hand rule, RHR.
Bf
Thumb = direction of conventional current
f
i e
ld
Fingers = point or curl in direction of
18/56
current
in direction of magnetic, B, field
AP Physics Rapid Learning Series - 17
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 10
Right Hand Rule for a Wire
Current
The thumb points in the direction of the current.
The fingers wrap around in the direction of a circular magnetic field
19/56
magnetic field.
Fields Into and Out of Page
Often it is necessary to symbolize fields that go into or out of the 2 dimensional page.
To represent a field coming directly out of the page:
20/56
x x xx x xx x x
To represent a field going into the page:
AP Physics Rapid Learning Series - 17
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 11
Visualization TipTo remember the notation for B fields going into and out of the page, think of an arrow.
When the B field is coming at you, out of the page, ld th ti A d t i d
21/56
you would see the arrow tip. A dot is used.
When the B field is going away from you, into the page, you would see the arrow feathers. An X is used.
Right Hand Rule for LoopsA loop carrying a current can be described using the right hand rule.
CurrentX X X X X X
X X X X
X X X X
. . .
. . .
. . .
22/56
X X X X
X X X X X X XThis gives a field going through and around the hoop as shown.
. . .
AP Physics Rapid Learning Series - 17
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 12
Force, current and B fieldsIf an electric current is passed through a wire that is already in a B (magnetic) field, it will experience a force.
A l
BiLsinθFB =
Force due to
magnetic field, N
Angle between i and B field
23/56
B field, T Length of wire, m
Current in wire, A
Effect of Angle
When using the formula FB=BILsinθ, the directions must be carefully considered.
Thus, if the current and B field are parallel,
θ = 0o, sin (0o) = 0
F = 0, minimum force
24/56
If the current and B field are perpendicular,θ = 90o, sin(90o) = 1F = BiL, maximum force
AP Physics Rapid Learning Series - 17
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 13
B Units
If you examine the previous formula, you will notice that B has units of N/(Am).
One Newton per Amp Meter is 1 Tesla, T.
1 Gauss = 1 x 10 -4 T
Obviously a Gauss is a small unit of magnetic field and a Tesla is a
25/56
of magnetic field, and a Tesla is a large one. The earth’s magnetic field is .5 G, or .5 x 10 -4 T .
Current Carrying Wire Example
Calculate the magnetic force on a high tension po er ire carr ing 1200 Apower wire carrying 1200 A of current.
Assume the wire is 100m long and situated at a 75°angle to the Earth’s magnetic field of 5x10-5 T.
26/56
AP Physics Rapid Learning Series - 17
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 14
Current Carrying Wire Solution
BiLsinθFB =
5 100m)sin75T)(1200A)((5x10F 5B
−=
5 8NF
00m)sin75)(1200A)(1AmN(5x10F 5
B−=
27/56
5.8NFB =
Notice that even with this very high current, the force is relatively small. Also, see how the units cancel out to yield Newton as the answer unit.
Right Hand Rule AgainFingers = direction of B field
Thumb = direction of conventional current
Line perpendicular to Palm = direction of forcep p
N S
FB
28/56
current
AP Physics Rapid Learning Series - 17
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 15
Force on a charge in B field
Sometimes there aren’t wires to carry current or charge. A lone electron may be flying through the air and encounter a B field. A similar effect happens, a force is exerted on the particle.
The RHR can be used again. Since the thumb
29/56
shows direction of conventional current, or + charge movement, if a negative particle is moving, then the thumb direction must be reversed.
Charge Moving in Field
B field into the pageX X X X X X
X X X X X X+velocity
V is to the leftX X X X X X
X X X X X X
X X X X X X
Force
V is to the left
F is downward
30/56
X X X X X X
This situation results in a centripetal force that keeps the particle moving in a circle.
At any point in time, v and F are perpendicular.
AP Physics Rapid Learning Series - 17
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 16
Another Force EquationThis formula calculates the force that acts on a charged particle moving in a B field.
Force due to A l
qvBsinθFB =
Force due to magnetic field, N
Angle between v and B field
31/56Force is a maximum when v is perpendicular to B
B field, TCharge, C Velocity, m/s
Movement of Electron
An electron is fired into a magnetic field that is going into the page as shown. How will it behave?
X X X X
e-
32/56
X X X X
X X X X
e
AP Physics Rapid Learning Series - 17
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 17
Direction of Negative Particle
Use the RHR, remember that conventional current flows opposite electron flow.
X X X X
X X X X
e-
FBFB
F
33/56
Initially, the force exerted on the particle is down. This makes it begin to curve. As it continues, the force is always pointing inward causing the electron to move in a clockwise circle.
FB
Calculation of Force ExampleThe magnitude of the force on this sample electron could be calculated. Assume the single electron moves at 1000 m/s through the B field of 0.5 T.
B i θF qvBsinθFB =
The charge on a single electron could easily be calculated or found in a reference text.
o19B 0)(.5T)sin9C)(1000m/s(1.6x10F −=
34/56
Nx10 8F 17B
−=
This small magnitude is the force exerted on the single electron moving through our example B field.
AP Physics Rapid Learning Series - 17
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 18
Size of Curve
The charged particle will travel in a circle. What factors do you think will affect the size, radius, of this circle?
The force causing the particle to turn acts as a centripetal force:
rmvF
2
c =
35/56
rThis force is magnetic in origin:
BF q v B sinθ=
Calculation of RadiusSet these two equations equal:
mvi θB2
rsinθBv q =
Since the v and B are perpendicular, sin θ=1
rmvB v q
2
=
36/56
qvBmvr
2
=
qBmvr =
AP Physics Rapid Learning Series - 17
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 19
Mass Spectrometer
A mass spectrometer can separate/identify various isotopes. They can also help identify various unknown chemical reactants.
Ions are accelerated by an electric potential. They are then flung into a magnetic field. Their paths help describe their properties.
37/56
A heavier object will curve less in the magnetic field, a lighter one will curve more.
Mass Spectrometer Diagram
. . . . . .B field out of paper
- Detector
. . . . . .
. . . . . .
of paper
m1 m2
38/56
Atoms with varying masses will travel different arcs. This “separates” or identifies isotopes with varying masses.
+ions+
AP Physics Rapid Learning Series - 17
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 20
B Field Due to a Straight WireOne would imagine that the B field from a current carrying wire is inversely proportional to the distance away from the wire.
πriμB o
2=
Current in wire, A
Constant,4∏x10-7Tm/A
39/56
πr2
B field, T
Perpendicular distance to
wire, m
μo
μo is known as the permeability of free space.
It is a constant that is similar to the one used in coulomb’s law εcoulomb s law, εo
ATm10 x 4πμ 7
o−=
40/56
Don’t confuse μo with the coefficient of friction, they are not the same.
AP Physics Rapid Learning Series - 17
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 21
B Field Diagram
In a simple one wire situation the magnetic field can be found atCurrent magnetic field can be found at any point using the RHR.
Consider how two parallel wires near each other might behave. The currents could be moving
41/56
either way also.
Two Current Carrying Wires
I1 I2 I1I
Use the RHR, current flowing in one wire, and the B field created from the other...
1 2 I1 2
42/56
Notice that if the current is in the same direction, the forces are attractive.
Also see how they are repulsive if the currents oppose each other.
AP Physics Rapid Learning Series - 17
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 22
B Field Away from Wire Example
In a typical household circuit, a wire usually carries no more than 15A of current. How strong is the magnetic field at point a distance of 10cm from this wire?
Current
43/56
10cmB=?
B Field Away from Wire Solution
πriμB o
2=
ATm10 x 4πμ 7
o−=
First, the distance given in centimeters must be changed into meters. This is necessary to match the meter unit in µo.
.10m100cm
1m x 10cm =
44/56
(.10m) 2π
)(15A)A
Tmx10 (4πB
7-
= T3x10 5−=
AP Physics Rapid Learning Series - 17
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 23
Magnetism inMagnetism in Nature and Technology
This section will explain several examples of magnetism in action You
45/56
examples of magnetism in action. You may be familiar with some of these.
Solar Magnetism
Because of the churning/dynamic nature of the sun, magnetic fields are abundant there.
Even a small telescope, equipped with the proper filter, can see magnetic eruptions on the surface.
46/56
This type of observation also shows that the sun is rotating.
AP Physics Rapid Learning Series - 17
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 24
Charged Projectiles
From solar eruptions like this, charged particles are thrown at the Earth.
47/56
These particles may become trapped in the Earth’s magnetic field and be seen as the northern or southern lights.
Audio SpeakersA speaker contains a permanent magnet, along with a coil of wire. When current runs through the coil, a magnetic field is formed.
48/56
The attraction or repulsion from the two fields moves a stiff paper cone that creates sound waves.
AP Physics Rapid Learning Series - 17
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 25
Large SpeakersIn general, larger magnets provide more force, thus moving more air and creating more sound. This means that larger/heavier speakers are usually better.
49/56
However, there are some more recent models that provide excellent performance in a compact package.
MRI
A relatively new type of biological imaging is Magnetic Resonance Imaging.
In this procedure, a patient is exposed to a very strong magnetic field. The protons in water atoms line up in this magnetic field.
50/56
Next, a radio pulse is sent in that tips the protons over a bit. When they right themselves, a faint signal is emitted.
AP Physics Rapid Learning Series - 17
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 26
MRI Images
MRI’s create rather detailed views even of soft structures that X rays often miss.
51/56
Unlike X rays, no ionizing radiation is used in an MRI scan.
Magnetic Media
Audio cassettes, VCR tapes and floppy disks all store information magnetically.
In each case, information is encoded onto a
52/56
substance that can be magnetized.
This information originates as an electric current that may come from a microphone, computer, etc.
AP Physics Rapid Learning Series - 17
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 27
More on Magnetic Media
This electric current is amplified, then sent to a recording head magnet that is near the audio, video, or computer tape.
As the current is varied the signal is etched or
53/56
As the current is varied, the signal is etched or imprinted onto the tape as a magnetic code.
This code persists even after it leaves the recording head magnet and is stored for later use.
B field caused by current:
B field caused by current:
iMagnetic force
on a moving Magnetic force
on a moving
Magnets contain
domains that
Magnets contain
domains that
Learning Summary
πriμB o
2=
Right Hand Rule RHRRight Hand Rule RHR
gcharged particle
FB=qvBsinθ
gcharged particle
FB=qvBsinθalign
themselves to create
magnetism
align themselves
to create magnetism
54/56
Right Hand Rule, RHRFingers = B field
Thumb = moving chargePalm = force
Right Hand Rule, RHRFingers = B field
Thumb = moving chargePalm = force
Magnetic force on a current carrying wire:
FB=BiLsinθ
Magnetic force on a current carrying wire:
FB=BiLsinθ
AP Physics Rapid Learning Series - 17
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 28
Congratulations
You have successfully completed the tutorial
Magnetic FieldsR id L i C tRapid Learning Center
Rapid Learning Center
Wh t’ N t
Chemistry :: Biology :: Physics :: Math
What’s Next …
Step 1: Concepts – Core Tutorial (Just Completed)
Step 2: Practice – Interactive Problem Drill
Step 3: Recap Super Review Cheat Sheet
56/56
Step 3: Recap – Super Review Cheat Sheet
Go for it!
http://www.RapidLearningCenter.com