Download Lecture 12:introduction to B fields, aurora

Magnetic Fields
Chapter 26
26.2 The force exerted by a magnetic field
Definition of B
26.3 Motion of a charged particle in a magnetic field
Applications
A circulating charged particle
Crossed fields: discovery of the electron
The cyclotron and mass spectrometer
The magnetic field
Magnetic field lines of
the earth depicted by
iron filings around a
uniformly magnetized
sphere.
William Gilbert discovered
that the earth is a natural
magnet in 1600.
Magnetic field lines
exit from the
north magnetic
pole. For the earth
this is the
geographic south
pole.
Magnetic force and field
The definition of B
B is defined in terms of the magnetic force
FB exerted on a moving electrically charged
particle.
Experimentally it is observed that, when a
charge q has velocity v in a magnetic field,
there is a force on the charge that is

proportional to q and to v,

greatest when charge moves
perpendicular to field, and zero
when parallel to the field – in
general it is proportional to the
sine of the angle between v and B.

perpendicular to both the velocity
and the field.
F  qv  B
Magnetic force and field
The definition of B
F  qv  B
SI unit of B is the Tesla
1T  1
N
 1N/(A.m)
C.m/s
1T  10 4 Gauss
The sign of q matters!
CHECKPOINT: An electron moves
perpendicular to a magnetic field.
What is the direction of B?
A. Left
B. Up
C. Into page
D. Right
E. Down
F. Out of page
Answer: C. For an electron the force is in
the direction of – (v x B)
November in Svalbard (Spitsbergen), 80° North
November near Melbourne (Australia), 37° South
Fine structure of the aurora
photos: Jan Curtis
field-aligned rays, multiple bands, different heights of the
lower border, and dynamics!
Aurora takes many
shapes and forms;
these are called
‘arcs’ and stretch
from one horizon
to another
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The lines within are
called rays
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This is called a
‘corona’ or crown; it
is the view looking
straight up the local
magnetic field line
(the magnetic
zenith)
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A particularly
bright and
beautiful aurora
in the magnetic
zenith
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– it’s fast!
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This view is about half the sky, using a
white light camera, at  3 speed
Two cameras superimposed, measuring
different wavelengths (colours)
9°, ~17km
1 frame/second color composite
Some questions:
what makes the
different colours?
how high is it?
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What is the aurora?
Fast incoming particles
strike oxygen and nitrogen
gases high in the
atmosphere, causing them
to make light of different
colours.
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Auroral Emission Lines
Spectrum of the Sun
Energy = h x frequency
Spectrum of the aurora
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Auroral Emission Lines
Spectrum of the Sun
Spectrum of the aurora
View from
500 km
the Space
Shuttle at
200 km
100 km
26.3 Motion of a point charge in a
magnetic field
The magnetic force is always perpendicular to the velocity
of the particle.
The magnetic force thus changes the direction of the
velocity but not its magnitude.
Therefore magnetic fields do no work on particles and do
not change their kinetic energy.
A circulating
charged
particle
The circular path of electrons
moving in the magnetic field
(into page) produced by two
large coils.
Charged particle moving in a
plane perpendicular to a
uniform magnetic field (into
page).
A circulating charged particle
False colour photo showing
tracks of a 1.6 MeV proton
(red) and a 7 MeV alpha
particle (yellow) in a cloud
chamber.
Radius of curvature is
proportional to the
momentum, and inversely
proportional to the charge.
Our active Sun
A movie from the TRACE instrument on the
SOHO satellite
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From the Sun to the Earth
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Sun-to-aurora TV analogy
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Helical paths
The path of the particle is a
helix.
Cloud chamber photo of helical
path of an electron in a magnetic
field.
Suppose that a charged particle enters a
uniform magnetic field with a velocity that is not
perpendicular to B. There is no force component,
and thus no acceleration component parallel to B,
so the component of the velocity parallel to B
remains constant.
Helical paths in a ‘magnetic bottle’ – and in the Earth’s field
Auroral emissions
seen from space:
the light occurs in two ring
shaped regions around each
magnetic pole. Charged
particles are guided there
by the magnetic field.
A string of auroral “substorms” following a Coronal Mass Ejection (CME)
impact on Earth
Observed by the University of Iowa’s VIS Imager on the Polar Satellite
Aurora on
other planets
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2 hours of data from
IMAGE satellite,
measuring Lyman
Alpha emissions in
ultraviolet from
precipitating protons
Svalbard
Svalbard
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Svalbard Radar
where we do some of our research into the aurora
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First results from new camera
ASK (Auroral Structure and Kinetics)
3 degree field of view in
magnetic zenith
Electric fields acting along the
magnetic field
22 October 2006
ASK1: 20 seconds of data at 32 fps
18:21:10 – 18:21:30 UT
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CHECKPOINT: Here are three
situations in which a charged
particle with velocity v travels
through a uniform magnetic field B.
In each situation, what is the direction
of the magnetic force FB on the
particle?
Answers: (a) +z (out)
A. Left
(b) –x (left, negative particle)
B. Up
C. Into page
(c) 0
D. Right
E. Down
F. Out of page
CHECKPOINT: The figure shows the circular
paths of two particles that travel at the
same speed in a uniform B, here directed
into the page. One particle is a proton; the
other is an electron.
p
e
(a) Which particle follows the smaller circle
A.
p
Answers: (a) electron (smaller mass)
B.
e
(b) Does that particle travel
A. clockwise or
B. anticlockwise?
(b) clockwise
Crossed magnetic
and electric fields
Net force:
F  qE  qv  B
The forces balance if
the speed of the
particle is related to
the field strengths by
qvB = qE
v = E/B (velocity selector)
Measurement of q/m
for electron
J J Thomson 1897
EXERCISE: Find an
expression for q/m
Sun-to-aurora TV analogy
A small part of the sky overhead
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