Our second exam is next Tuesday – Nov 1. It will cover everything I have covered in
class including material covered Thursday.
There will be two review sessions Monday, Nov 1 - at 12:30 PM and at 3:00 PM in
the same room as the problem solving session: FN 2.212.
I will put several review questions/problems on Mastering Physics. These are not for
credit but for practice. I will review them at the review session Monday.
Magnetic Poles vs Electric Charge
The interaction between magnetic poles is similar to the Coulomb
interaction of electric charges BUT magnetic poles always come in
pairs (N and S), nobody has observed yet a single pole (monopole).
Despite numerous searches, no evidence of magnetic charges exist.
In other words, there are no particles which create a radial magnetic
field in the way an electric charge creates a radial field.
Magnetic Field
Electric charges produce electric fields E and, when
they move, magnetic fields B
In turn, charged particles experience forces in those
fields:
Lorentz force acting on charge q moving with velocity
v in electric field E and magnetic field B
F  q (E  v  B )
For now we will concentrate on how magnetic force affects
moving charged particles and current-carrying conductors…
Like electric field, magnetic field is a vector field, B
Magnetic Forces on Moving Charges
Force F is perpendicular to the plane of v and B
and numerically equal to
F  q v B  q vB sin 
Direction of F is specified as follows

 
F  q v B
Unit for magnetic field :
N
N
1 Tesla (T) 

C  m/s A  m
1 T  10 4 Gauss (G)
The right hand rule is a useful mnemonic for visualizing the direction of a magnetic force
as given by the Lorentz force law. The diagrams above are two of the forms used to
visualize the force on a moving positive charge. The force is in the opposite direction for
a negative charge moving in the direction shown. One fact to keep in mind is that the
magnetic force is perpendicular to both the magnetic field and the charge velocity, but that
leaves two possibilities. The right hand rule just helps you pin down which of the two
directions applies.
Measuring Magnetic Fields with Test Charges
Total force with both electric and
magnetic fields acting on the charge q


Example: Magnetic force on a proton
Beam of protons moves at v=300000 m/s
through a uniform field B=2.0 T at an angle
30 degrees relative to the field direction
 
F  q( E  v  B )
Alternative rule – direction of right-hand-thread
screw would advance when turned in the same
direction as rotation of vector v toward B for a
positive charge

B
-

v
Which direction does the charge deflect?
a)Up
b)Down
c)It keeps going straight
Magnetic field does NO work; only the
direction of the velocity changes, not its
magnitude!
Application: The Mass Spectrometer
An atom or molecule is ionized by knocking one or
more electrons off to give a positive ion. This is true
even for things which you would normally expect to
form negative ions (chlorine, for example) or never
form ions at all (argon, for example). Mass
spectrometers always work with positive ions.
The ions are accelerated so that they all have the same
kinetic energy.
The ions are then deflected by a magnetic field
according to their masses. The lighter they are, the more
they are deflected.
The amount of deflection also depends on the number
of positive charges on the ion - in other words, on how
many electrons were knocked off in the first stage. The
more the ion is charged, the more it gets deflected.
The beam of ions passing through the machine is
detected electrically.
TEGA ovens
The Phoenix Mass Spectrometer
Scoop dumping martian soil into a
TEGA oven
10
Peak Rate (counts/sec)
10
10
10
10
10
6
Sweep #18
6/4/2008 03:49:09
SOL 9 / 14:37:24
TEGA secs = 13308
Channel 1
Channel 2
Channel 3
Channel 4
5
4
3
2
1
C:Documents and Settings:John:My Documents:TEGA runs-new:Sol_009_tega_atmos.r32_V240:Graph6
15
20
25
30
Mass
35
40
45
TEGA mass spectrum
Note 6 decade log scale on Y axis
Largest peaks from CO2 and CO and their isotopes, 13C and 18O,
O and C peaks from CO2. Mass 40 peak is Ar.
Other peaks are multiply charged ions and residuals.
Evidence of water on
Mars from TEGA
Mass Spectrometry in Medical Research and Diagnostics
Important tool for proteomics, the analysis of the whole range of proteins expressed in a cell.
• identify proteins and to determine their amino acid sequence.
• used to determine if a protein has been modified by the addition of phosphate groups or
sugars
• allows other molecules, including DNA, RNA, and sugars, to be identified or
sequenced.
Diagnostic tool in clinical treatment, infectious pathogen research, neonatal diagnostics,
cancer, brain and allergy research
Used in various fields of medicine: cardiology, pulmonology, neurology, psychiatric diseases,
hemato-oncology, urologic diseases, gastrointestinal diseases, gynecology and pediatrics.
Other examples:
• Neonatal screening for congenital metabolic disorders
• Therapeutic drug monitoring, among others monitoring of immunosuppressive drugs,
antimycotic drugs, antiepileptic drugs, antiviral drugs
• Androgen profile
• Carnitine analysis
• Sulfonylurea screening
• Fatty acid analysis (diagnosis of Refsum's disease,adrenoleukodystrophy)
• Cannabinoid confirmation test
• Methylmalonic acid in urine or serum (diagnosis of vitamin B12 deficiency)
Magnetic Field Lines
IMPORTANT – Magnetic field lines are NOT
lines of force !!!
The force is always perpendicular
to magnetic field lines.
Sources of Magnetic Fields and Field Lines
If magnetic fields exert forces on moving electric charges, then moving electric charges
create magnetic fields, i.e. currents produce fields.
Follows right-hand rule: point thumb of right
hand in direction of current - magnetic field
curls around wire in direction of curled
fingers
If the current flows in a loop,
the magnetic field produced is
like a bar magnetic - curl
fingers of right hand in
direction of current flow north pole is in direction of
thumb.
Sources of Magnetic Fields and Field Lines
The electron spins on its axis, giving rise to a electron
current in the direction of rotation. Think of the electron
as a ball with charge distributed over its surface. When
the ball spins, that charge is set in motion around the
electron's spin axis, resulting in a magnetic field specific
to the electron.
The electron is like a magnetic dipole, a miniature
magnet, with a north end and a south end.
In most substances, electrons spin in random directions - magnetic fields cancel. For iron
and other magnetic substances, the spin magnetism is not canceled. Can be permanently
magnetized by placing in strong magnetic field and permanently aligning atoms - can be
demagnetized by dropping magnet and jostling atoms out of alignment.
Electromagnetic produced by wrapping coil around
iron bar - magnetic field produced that aligns atoms
in bar - more coils or more current - larger magnetic
field and greater atomic alignment
Motion of Charged Particles in a Magnetic Field
Magnetic field keeps particle rotating with conserved magnitude of v :
mv2
mv
FB  qv B 
; r 
r
qB
2r 2m
2 qB
Period T 

; 

independen t of v !
v
qB
T
m
(cyclotron frequency)
v|| is not affected by the field - a helical trajector y
The Cross Product
i, j, and k are unit vectors in the x, y, and z directions
i×j=k
j×k=i
k×i=j
Given vectors a and b such that
a = a1i + a2j + a3k = (a1, a2, a3)
b = b1i + b2j + b3k = (b1, b2, b3)
a × b = (a2b3 − a3b2) i + (a3b1 − a1b3) j + (a1b2 − a2b1) k = (a2b3 − a3b2, a3b1 − a1b3, a1b2 −
a2b1)
In matrix form
i j k
a  b = a1 a 2 a 3
b1 b 2 b 3
The solid vertical bars
around the matrix means
the determinant of the
matrix
a × b = ia2b3 + ja3b1 + ka1b2 – ia3b2 – ja1b3 – ka2b1
or
a2 a3
a1 a 3
a1 a 2
a  b =
i j +
k
b2 b3
b1 b3
b1 b2
The magnitude of the cross product is
a  b = a b cos
where θ is the angle between a and b

Particle moving in uniform magnetic field: Coordinate analysis
Let
B  (0,0, B); v  (v x , v y , v z )
dvx
 q ( v  B) x  q (v y Bz  v z B y )  qv y B
dt
dv y
m
 q ( v  B) y  q (v z Bx  v x Bz )  qv x B
dt
m
m
dv z
 q ( v  B) z  q (v x B y  v y Bx )  0  v z  v||  const
dt
2
d 2 v x qB dv y
qB
 
2



v



vx


x
2
dt
m dt
 m
dx
 v x  v cos(t   0 ) 
dt
 x  x0  r sin( t   0 ), r  v / 
Both position and velocity in  plane exhibit harmonic
sinusoidal time evolution
Example: Helical particle motion
Proton (m=1.67*10-27 kg) moves in a uniform
magnetic field B=0.5 T directed along x-axis
at t=0 the proton has velocity components
vx  1.5  105 m / s
vy  0
vz  2  105 m / s
a) At t=0 find the force on the proton
and its acceleration.
b) find the radius of the helical path and
the pitch of the helix
v  vz
a

F  qvz  B  qvz B j
F
 9.58  1012 m / s 2
m
R
mvz
 4.18 mm
qB
qB
 4.79  107 rad / s
m
2
T
 1.31  107 s


pitch  vxT  19.7 mm
Particles in non-uniform magnetic fields
Magnetic bottle to trap particles
Used to contain high temperature plasmas that would vaporize any material container
• magnetic confinement is one of two major branches of fusion energy research –
used in magnetic fusion energy devices such as tokamaks,
The Earth’s Magnetosphere
Earth can be viewed as a gigantic bar magnet spinning in space.
• Its toroidal magnetic field encases the planet like a huge inner tube.
• This field shields Earth from the solar wind—a continuous stream of charged particles
cast off by the sun.
 Produces a bullet-shaped cavity called the magnetosphere.
 It also traps charged particles – leads to the radiation or Van Allen belts.
The Earth’s Radiation Belts
Particles are trapped by the non-uniform geomagnetic field – much like a magnetic bottle
– they bounce back and forth from one hemisphere to another.
The trapped particles tend to congregate in distinct bands based on their charge, energy,
and origin.
Two primary bands of trapped particles exist: the one closer to Earth is
predominantly made up of protons, while the one farther away is mostly electrons.
The South Atlantic Anomaly
Count rate of protons and electrons > 0.5 MeV in low Earth orbit
Magnetic north and geographic north do not exactly line up - Earth's magnetic dipole is tilted by
about 11.5 degrees from its rotational axis and shifted slightly off-center.
•At the north magnetic pole, field is stronger - effectively keeps inner proton belt farther away
•At the south magnetic pole, field is weaker, allowing the proton belt to come closer to the
Earth – i.e., bounce point or mirror point of particles closer.
Most of the proton belt is about 1200 –1300 km high, but it dips down as low as 200–300 km off
the lower coast of Brazil where magnetic field weakest, creating a phenomenon known as the
South Atlantic Anomaly (SAA).
This radiation can cause all sorts of malfunctions in spacecraft electronics. A satellite in a typical
low Earth orbit (< ~ 750 km) remains safely below the proton belt—except at the SAA.
NASA’s Terra Earth Observing System satellite's high-gain antenna periodically went into "safe"
mode, interrupting communications. Tests indicated that an anomalously high current had passed
through the motor drive assembly. If fact, no high current—only a glitch in a semiconductor
component that made it look as though a high current had occurred.
• Result of a single-event upset, an error caused by the action of ionized particles –
generated by radiation belt protons. Nearly 50 percent occurred in the SAA, whereas only 5
percent of orbital time was spent there.
Problem for numerous low-altitude spacecraft
• Hubble turns off in SAA
• Astronauts avoid EVA activities as much as possible in SAA – radiation exposure
Near the poles, energetic particles stream down magnetic field lines into the atmosphere - generate
the aurora (aurora borealis/northern lights in the northern hemisphere and aurora australis/southern
lights in the southern hemisphere). In the picture, you can actually “see” the magnetic field lines.