Download magnetism - Earth and Environmental Sciences

1
Natural Sciences I
lecture 12: more Electricity & Magnetism
MAGNETISM
Scientific curiosity about magnetism goes back to at least 600 B.C. to the
Greeks' observations of the properties of lodestone, which included th
following:
N
The two "poles"
orient themselves
more-or-less north
and south in the
Earth's magnetic
field – hence the
"N-S" designations
we still use today.
lodestone
iron particles
Before we go further, let's get ourselves oriented with respect to the Earth's
magnetic field...
o
22 E
o
o
20 E
18 W
o
18 E
o
10 W
o
16 E
o
6W
o
14 E
o
12 E
o
10 E
Magnetic declinations
indicate the location of the magnetic
north pole relative to true north
o
8E
o
6E
o
4E 2E
o
0
o
2
Earth's magnetic field
magnetic north
geographic
(true) north
The geographic and magnetic north poles are not
located in exactly the same
place.
N
We describe the
orientation of the Earth's
magnetic field at a given
location in terms of a
magnetic declination (p. 1)
and a magnetic dip. The
dip is horizontal at the
magnetic equator and
vertical at the north and
south magnetic poles.
S
You are now familiar with the manner in which we represent the lines of force
of an electric field. A Similar approach is used for magnetic fields...
lines of force
N
S
arrowheads indicate
direction in which the
north pole of a small
magnet would point
The magnetic field is analogous the electric field surrounding an electric
charge and the gravity field surrounding a massive object. Like these other
two force fields, a magnetic field results in "force at a distance" effects.
An additional similarity with electric fields, of course, is that opposite poles
attract and like poles repel – as is the case with electric charges.
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Source of Magnetic Fields
Despite the similarities noted on page 2, magnetic fields have
properties that signal obvious differences from electric fields. Recall that
an electric field is caused by a local excess of positive or negative charge
(i.e, an overabundance or deficiency of electrons). A magnetic field, in
contrast, is not caused by localization of north or south poles on an object.
One way to demonstrate this fact is to cut up a bar magnet into
progressively smaller pieces. No matter how hard you try, you will only
produce shorter versions of the same magnet – i.e., you will not succeed in
isolating a north or south pole (a magnetic monopole).
S
N
S
S
N
S
N
S
N
S
N
N S
N
S N S N S N S N S N S N S N S N
magnetic poles come
only in pairs (electric
charges can be paired, but
they don't have to be)
Magnetism is now understood to be produced by electric currents – it
is a secondary property of electricity. The first big breakthrough was made
by a Danish physicist, Hans Christian Oersted, in 1820. Interestingly, his
discovery was largely accidental, made during a lecture/demonstration to
students gathered around a table. Here's a more elaborate representation
of Oersted's unplanned experiment...
compasses
( )
conventional
current
(+)
When the wire (red)
is connected to the
battery, the compass
needle aligns itself
perpendicular to the
wire, pointing in the
direction given by
the "right-hand rule"
(thumb pointing in
the direction of conventional current
flow).
4
The right-hand rule is used
to determine the direction of
magnetic field lines around a
conventional current (flow
of positive charges)
The left-hand rule is used
to determine the direction of
magnetic field lines around
an electron current
When the thumb is pointing in the direction of flow, the curled
fingers reveal the orientation of the magnetic field.
Current in a loop:
The red arrows show
the magnetic field lines
at various points. Which
"kind" of current (electron
or conventional) is shown?
(+)
( )
5
What Oersted discovered is that electric current produces a magnetic field,
suggesting for the first time that magnetism is a property of moving
electric charges. A stationary charge produces only an electric field;
charges in motion produce a magnetic field to accompany the electric field.
Just as a gravitational field is a property of the space surrounding a mass
and an electric field is a property of space surrounding a charge, a
magnetic field is a property of space surrounding a moving charge (and the
strength of the magnetic field is proportional to the speed at which the
charge is moving).
Digression on permanent magnets...
Something seems amiss here. If magnetic fields result from charges
in motion, what's the story with permanent magnets – such as bar magnets,
horseshoe magnets, and those we use to post stuff on our refrigerators?
There is no current flowing through these, so where does the magnetic field
come from?
The key to this
apparent paradox is that
all atoms consist of
charged particles (electrons and protons), and
the electrons of every
atom are in motion about
the nucleus. Since they
are moving charges,
these electrons create
magnetic fields.
(Note: This is a
cartoon. It is not
intended to be an
accurate representation, but to
convey an idea)
In most materials, the tiny magnetic fields cancel one another, so the
overall object exhibits no magnetic properties. In a few materials, however,
the atoms are oriented in such a way that their individual magnetic fields
can act in unison to impart magnetic properties to the overall structure.
Examples of such materials are iron and some of its oxides, nickel, cobalt
and rare earth elements.
In a permanent magnet, the atoms are grouped in small regions
called magnetic domains, and these domains are aligned with one
another to create the overall magnetic field.
(next page)
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Permanent magnets (cont'd)
UNMAGNETIZED IRON
individual magnetic domains
(~0.01 to 1 mm in size)
orientations random
MAGNETIZED IRON
orientation of magnetic
domains mostly aligned
N
When unmagnetized iron is placed in a magnetic field, the domains
aligned with that field grow at the expense of those that are not aligned
Digression on natural permanent magnets
Permanent magnets are formed in nature in at least three ways (all involve
the iron oxide magnetite – Fe3O4)
All molten rocks contain
some iron oxide. This
forms crystals as the
lava cools, some of
which are magnetite.
When the magnetite
cools below its Curie
o
temperature (~500 C),
it becomes magnetized
in alignment with the
Earth's magnetic field.
corbis.com
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Sedimentary rocks can also acquire permanent magnetism (called
natural remanent magnetism), but by a quite different mechanism. Most
sedimentary rocks are formed from rock and mineral particles settling that
have settled to the bottom of a water body. Some of these particles are
magnetite (Fe3O4), and if they settle in a "gentle" environment, they can
orient themselves in the Earth's magnetic field. The resulting sedimentary
rock thus records the location of the magnetic pole (which moves around
over geologic time).
N
N
S
The rock that eventually forms from this
sediment will contain
innumerable tiny
magnets, all pointing
in the same direction
Other natural permanent magnets: Navigational and "orientational" uses
by organisms; for example
migratory birds
magnetotactic bacteria (apparently use internal magnetite grains to
distinguish up from down)
8
...back to ELECTRIC CURRENTS and MAGNETISM
Current loops
As we learned on page 3, electric current flowing in a wire creates a
magnetic field around that wire. This leads to some interesting possibilities
if we bend the wire or bring it close to other current carrying wires...
First, a single loop:
e
e
Because of the
orientation of the
magnetic field
lines passing
through the loop,
the two sides of
the loop will have
different poles.
Can you tell which
pole the front side
of the loop has?
A current passing through a cylindrical coil (a solenoid) causes the coil to
act like a bar magnet:
(+)
These suspended batteries
orient themselves in the
magnetic field of a bar magnet
(Ampere showed this in 1820s)
( )
N
S
( )
(+)
S
N
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( )
N
The magnet pictured here
is an electromagnet. Unlike a bar magnet, the
magnetic field can be
turned on and off by connecting or disconnecting
the battery. Moreover, the
strength of the field can be
varied by changing the
current or the number of
loops in the solenoid.
(+)
S
The discovery of the elec-tromagnet and description
of its properties by Andre
Ampere in the 1820's
created the possibility of
doing mechanical work
with an electrical device.
There are numerous applications of electromagnets
that you can read about in
your text (see p. 131ff).
Some examples are discussed on page 12...
The main lesson of the last few pages is that current flowing through a
wire creates a magnetic field. If the wire is formed in a loop or coil, the
resulting magnetic field has a poles like a bar magnet. Two other
observations follow:
the magnetic fields produced by two different current-carrying wires or
current loops interact with one another (Ampere worked out the
relationships)
if a loop of wire is moved in a magnetic field, a current is induced in the
wire – ELECTROMAGNETIC INDUCTION
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ELECTROMAGNETIC INDUCTION
Following quickly on the contributions of Oersted and Ampere to our
understanding of magnetism came the further discovery that a coil of wire
moving through a magnetic field develops a potential difference (a voltage)
along its length. This is called an induced voltage, and it leads to flow of
electrons (current). Current can also be induced in a coil by varying the
strength of a magnetic field in which the coil sits. These induction
phenomena were discovered simultaneously (and independently) in 1831
by Joseph Henry in the U.S. and Michael Faraday in England.
Here's a simple demonstration...
S
amps
0
N
S
Moving the
magnet through
the coil induces
a current
through the coil.
Changing the
direction of
motion changes
the direction of
current flow.
amps
0
No current is
detected if
the magnet is
not moving
N
11
Here's the device Faraday first used to demonstrate
electromagnetic induction:
switch
amps
0
primary coil
(insulated wire)
iron
ring
secondary coil
(insulated wire)
Immediately upon closing the switch, Faraday noticed a brief flicker of
current in the secondary coil, but none thereafter. As the magnetic field
was being established in the iron ring (i.e., when the field lines were
moving), a current was induced in the secondary coil. However, once the
magnetic field in the ring became stable (very quickly!), there was no
induced current. This observation led Faraday to the realization that the
magnetic field has to be moving in order for induction to work.
Question of the day: What would have happened if
Faraday had used an electrical outlet rather than a
battery?? (OK, so he didn't have any outlets handy)
Demonstrations like the preceding ones can be used to show that
electromagnetic induction occurs when the coils of wire move across
magnetic field lines (or vice versa: it doesn't matter which one moves as
long as there is relative motion between the magnetic field lines and the
coil). The induced voltage depends upon:
the number of loops (the more loops, the higher the voltage)
the rate of relative motion
the strength of the magnetic field
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Two EXAMPLES of devices that use electromagnetic induction...
A simple dynamo (AC generator)
As it rotates, the wire loop (green)
crosses the magnetic field lines in
alternating directions. The resulting
current in the loop therefore flows
first in one direction, then the other.
magnet
field lines
S
rotation
R
N
output
(voltage or
direction of
current flow)
rotation angle
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The transformer
As noted in the last lecture, Thomas Edison was an advocate of DC
power for commercial and domestic use, but ultimately AC power was
adopted instead. A principal reason was that AC power can readily be
stepped up and down in voltage for different applications (it can also be
transmitted over long distances more efficiently).
Although he didn't use it in this way, the device built by Faraday (page
11) demonstrates the great advantage of AC power over DC power: it is a
crude transformer. With direct current flowing in the primary coil, however, it
works as a transformer only for a fleeting moment when the current is first
turned on. This is the only time when the magnetic field created in the iron
ring is changing. If the current in the primary coil were AC, then a stable
alternating current would be established in the secondary coil as well...
Step-down transformer
SECONDARY
PRIMARY
120 V
10 loops
1 loop
12 V
voltsprimary
voltssecondary
=
loopsprimary
loopssecondary
power input = power output
Step-up transformer
watts input = watts output
(amps volts)in = (amps volts)out
1 loop
1200 V
120 V
10 loops
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Calculations with transformers – Examples
1. A step-up transformer has 10 loops on its primary coil and 40 loops on
its secondary coil. If the primary coil is supplied with AC current at 120 V,
what is the voltage on the secondary coil?
NP = 10 loops
NS = 40 loops
VP = 120 V
VS = ?
VS
VP
=
NS
NP
VS =
VS =
VPNS
NP
(120 V) (40 loops)
10 loops
= 480 V
2. The primary coil of the step-up transformer in example 1 is supplied
with 10 amps of AC current at 120 V. What current flows in the secondary
coil?
VP = 120 V
IP = 10 A
VPIP = VSIS
IS =
VPIP
VS
IS =
(120 V) (10 A)
480V
VS = 480 V
IS = ?
= 2.5 A
The same amount of electrical energy can be carried at a lower current
(reducing loss due to resistance) when a higher voltage is used (power
= amps x volts). This is why very high voltage transmission lines
(50,000 or more volts) are used to carry electrical energy from
generating facilities to consumers. Such voltages are way too high for
normal uses, so they are stepped way down with transformers.
15
Back to Earth...
source of the Earth's magnetic field
magnetic field lines
outer core
(molten iron + nickel)
CONVECTING
inner core
(solid iron + nickel)
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The Earth’s magnetic field is now understood to work like
a “self-exciting” dynamo...
dynamo
magnetic
field lines
metal disk
(e.g., copper)
S
permanent
magnet
The magnetic
field induces the
radial current in
the disk.
amps
N
0
“self-exciting” dynamo
magnetic
field lines
electromagnet
(coil)
amps
0
The magnetic
field induces the
radial current in
the disk; the
current flowing
through the coil
sustains the
magnetic field.