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

)( BvEF q

Lorentz force acting on charge q moving with velocity v in electric field E and magnetic field B

Electric charges produce electric fields E and, when they move, magnetic fields B

In turn, charged particles experience forces in those fields:

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

sinF q v B q vB

Force F is perpendicular to the plane of v and B and numerically equal to

Direction of F is specified as follows

F q v B

(G) Gauss 10T 1

mA

N

m/sC

N(T) Tesla 1

:field magneticfor Unit

4

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

( )F q E v B

Total force with both electric andmagnetic fields acting on the charge q

Example: Magnetic force on a protonBeam of protons moves at v=300000 m/sthrough a uniform field B=2.0 T at an angle30 degrees relative to the field direction

Alternative rule – direction of right-hand-threadscrew would advance when turned in the same direction as rotation of vector v toward B for a positive charge

Magnetic field does NO work; only the direction of the velocity changes, not its

magnitude!

B

v-

Which direction does the charge deflect?a)Upb)Downc)It keeps going straight

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

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.

101

102

103

104

105

106

Pe

ak R

ate

(co

unt

s/se

c)

45403530252015Mass

C:Documents and Settings:John:My Documents:TEGA runs-new:Sol_009_tega_atmos.r32_V240:Graph6

Channel 1 Channel 2 Channel 3 Channel 4

Sweep #186/4/2008 03:49:09SOL 9 / 14:37:24

TEGA secs = 13308

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 researchUsed 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 perpendicularto magnetic 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

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

y trajectorhelical a - field by the affectednot is

frequency) (cyclotron

! oft independen 2

;22

Period

;

: of magnitude conserved with rotating particle keeps field Magnetic

||

2

v

vm

qB

TqB

m

v

rT

qB

mvr

r

mvBqvF

v

B

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)

€

a × b =

i j k

a1 a2 a3

b1 b2 b3

a × b = ia2b3 + ja3b1 + ka1b2 – ia3b2 – ja1b3 – ka2b1

€

a × b = a2 a3

b2 b3

i - a1 a3

b1 b3

j + a1 a2

b1 b2

k

In matrix form

or

The Cross Product

The magnitude of the cross product is

where θ is the angle between a and b

€

a × b = a b cosθ

The solid vertical bars around the matrix means the determinant of the matrix

Particle moving in uniform magnetic field: Coordinate analysis

evolution timesinusoidal

harmonicexhibit plane in velocityandposition Both

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)cos(

const0)()(

)()(

)()(

),,();,0,0(Let

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0

22

2

2

||

vrtrxxdt

dxtvv

vvm

qB

dt

dv

m

qB

dt

vd

vvBvBvqqdt

dvm

BqvBvBvqqdt

dvm

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dvm

vvvB

x

xxyx

zxyyxzz

xzxxzyy

yyzzyxx

zyx

Bv

Bv

Bv

vB

Example: Helical particle motionProton (m=1.67*10-27 kg) moves in a uniformmagnetic field B=0.5 T directed along x-axisat t=0 the proton has velocity components

5

5

1.5 10 /

0

2 10 /

x

y

z

v m s

v

v m s

a) At t=0 find the force on the protonand its acceleration. b) find the radius of the helical path and the pitch of the helix

zv v z zF qv B qv B j

12 29.58 10 /F

a m sm

7

7

4.18

4.79 10 /

21.31 10 s

19.7

z

x

mvR mm

q B

q Brad s

m

T

pitch v T mm

Particles in non-uniform magnetic fieldsMagnetic 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.

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 Earth’s Radiation Belts

The South Atlantic Anomaly

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).

Count rate of protons and electrons > 0.5 MeV in low Earth orbit

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.