Our second exam is next Tuesday – Nov 1. It will cover everything I have covered in class including material covered today. You will be allowed one 8 ½ X 11 sheet of notes; both sides of the sheet may be used.. You should put any formulas/information on these notes that you think will help you on the exam.

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 have 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.

The extra credit problems are now on Mastering Physics. They will be due by 10:59 PM on Dec 13.

Particle moving in uniform magnetic field: Coordinate analysis

evolution timesinusoidal

harmonicexhibit plane in velocityandposition Both

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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

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12 29.58 10 /F

a m sm

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q B

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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.

Magnetic Flux

Magnetic flux is defined similarly to electric flux:

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Magnetic flux through an area dA is

dΦB = B⊥dA = BcosφdA =r B • d

r A

Total magnetic flux through a surface is

ΦB = B⊥dA = BcosφdA =r B • d

r A ∫∫∫

SI unit of magnetic flux is the Weber:

1Wb=1Tm2

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The total magnetic flux through a closed surface

is always zero :r B • d

r A = 0∫

Gauss’s law for magnetism:

There are no isolated magnetic charges or monopoles.

Velocity selector and mass spectrometer

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q

m

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cities with veloparticlesonly are dUndeflecte

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Magnetic Force on a Current-Carrying Conductor

Straight segment of wire

Summing up forces on individual

charge carriers:

( ) ( )( )B d dq nAl nq A l F v B v B

F IlB

F I l B

Magnetic force on a straight wire segment

dF I dl B

On an infinitesimal wire section

)dependent-position

becan and (

:segments

individualon forces up Summing

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BsF

d

dIb

a

B

Example: Force on a curved conductor

( )dF I Rd B

0

0

cos 0

sin 2

x

y

F IRB d

F IRB d IRB

( 2 )F IB L R

Forces and Torques on the Current Loop

' sin(90 ) cos

F IaB

F IbB IbB

Net force is zero

The Torque is not zero

2 ( / 2)sin ( )( sin )

sin

F b IBa b

IBA