l20 ch29 cyclotron motion · the cyclotron the first practical particle accelerator, invented in...

PHYS.1440Lecture20 A.DanylovDepartmentofPhysicsandAppliedPhysics

Lecture 20

Chapter 29

Cyclotron motion

Physics II

Messiah!?…Miraculous appearance

out of the blue.

Course website:https://sites.uml.edu/andriy-danylov/teaching/physics-ii/

PHYS.1440Lecture20 A.DanylovDepartmentofPhysicsandAppliedPhysics

Today we are going to discuss:Chapter 29:

Section 29.7 (Skip the Hall effect) Section 29.8 Section 29.5 Skip

PHYS.1440Lecture20 A.DanylovDepartmentofPhysicsandAppliedPhysics

Cyclotron Motion

Manyimportantapplicationsofmagnetisminvolvethemotionofchargedparticlesinaperpendicularmagneticfield

There is an amazingly beautiful application of 

PHYS.1440Lecture20 A.DanylovDepartmentofPhysicsandAppliedPhysics

Cyclotron motion

Thefigureshowsapositivechargemovinginaplanethatisperpendiculartoauniformmagneticfield.

B into page

Since F isalwaysperpendiculartov,F changesthedirectionofthevelocity,butnotitismagnitude.Itmeansq experiencesonlythecentripetalaccelerationThus,thechargeundergoesuniformcircularmotion.

Thismotioniscalledthecyclotronmotionofachargedparticleinamagneticfield.

PHYS.1440Lecture20 A.DanylovDepartmentofPhysicsandAppliedPhysics

Cyclotron radius

B

Newton’s second law for the radial direction,

The frequency of the cyclotron motion.

The radius of the cyclotron orbit:

The period of the cyclotron motion: 2 1

2

If B=0, then rcyc=, which is a straight line

Note! The cyclotron frequency does not depend on v.

2 2

PHYS.1440Lecture20 A.DanylovDepartmentofPhysicsandAppliedPhysics

Cyclotron motion (general situation)

B

∥

Thefigureshowsamoregeneralsituationinwhichthechargedparticle’svelocityisnotexactlyperpendiculartoB.

Thecomponentof v paralleltoBisnotaffectedbythefield,sothechargedparticlespiralsaroundthemagneticfieldlinesinahelicaltrajectory.

Theradiusofthehelixisdeterminedbyv,thecomponentofvperpendiculartoB.

PHYS.1440Lecture20 A.DanylovDepartmentofPhysicsandAppliedPhysics

Aurora (Northern lights)

Charged particles(solar wind)

Van Allen radiation belthttps://en.wikipedia.org/wiki/Van_Allen_radiation_belt

PHYS.1440Lecture20 A.DanylovDepartmentofPhysicsandAppliedPhysics

The Cyclotron

Thefirstpracticalparticleaccelerator,inventedinthe1930s,wasthecyclotron.

Cyclotronsremainimportantformanyapplicationsofnuclearphysics,suchasthecreationofradioisotopesformedicine.

Therelevantequationforusis:.

Accordingtothisequation,the

biggerthecharge,thesmallertheradius.

ConcepTest Mass Spectrometer x x x x x x x x x x x xx x x x x x x x x x x xx x x x x x x x x x x xx x x x x x x x x x x xx x x x x x x x x x x xx x x x x x x x x x x xA B

Twoparticlesofthesamemass enteramagneticfieldwiththesamespeedandfollowthepathsshown.Whichparticlehasthebiggercharge?

C)bothchargesareequalD)impossibletotellfromthepicture

Follow-up: What is the sign of the charges in the picture?

If q > 0, then the force is to the left (our case)

, , ,

PHYS.1440Lecture20 A.DanylovDepartmentofPhysicsandAppliedPhysics

Cloud/Bubble chamber to detect charged particles

(contains a supersaturated vapor of water)The photograph shows the track of anunusual positively charged particle with amass about equal that of an electron sloweddown by passing through a lead plate. Itwas among the earliest evidence of theexistence of the positron found by C.D.Anderson in 1932, but predicted by PaulDirac in 1928

lead plate

A gamma photon kicks out an electron out of an atom and creates an electron‐positron pair.

PHYS.1440Lecture20 A.DanylovDepartmentofPhysicsandAppliedPhysics

Magnetic force on Current-Carrying Wires

PHYS.1440Lecture20 A.DanylovDepartmentofPhysicsandAppliedPhysics

Magnetic Forces on Current-Carrying Wires

Wesawthatamagneticfieldexertsaforceonacharge.Acurrentconsistsofmanymovingcharges,soamagneticfieldshouldexertaforceonacurrent.

The magnetic force on a segment dl:

The magnetic force of a charge:

If we apply this formula for a straight wire with a current I, then we will get:

Where l is a part of wire exposed to the magnetic field

End of class

PHYS.1440Lecture20 A.DanylovDepartmentofPhysicsandAppliedPhysics

There’snoforceonacurrent‐carryingwireparalleltoamagneticfield.

Magnetic Forces on Current-Carrying Wires

∥

PHYS.1440Lecture20 A.DanylovDepartmentofPhysicsandAppliedPhysics

A current perpendicular to the field experiences a force in the direction of the right-hand rule.

Magnetic Forces on Current-Carrying Wires

PHYS.1440Lecture20 A.DanylovDepartmentofPhysicsandAppliedPhysics

Magnetic Forces Between Parallel Current-Carrying Wires: Current in Same Direction

We’ll treat I2 as a source of the magnetic field

Let’s find a force on current I1

Demo: Forces on a Current‐Carrying Wire

PHYS.1440Lecture20 A.DanylovDepartmentofPhysicsandAppliedPhysics Slide 32-147

Magnetic Forces Between Parallel Current-Carrying Wires: Current in Opposite Directions

PHYS.1440Lecture20 A.DanylovDepartmentofPhysicsandAppliedPhysics

SummaryElectric Field Magnetic Field

Amperian loop

The magnetic force on a charge:

The magnetic force on a current:

From Coulomb’s law1

4̂

Bio-Savart law

4̂

Gauss’s Law

∙ ∙

The electric force on a charge:

PHYS.1440Lecture20 A.DanylovDepartmentofPhysicsandAppliedPhysics

Thank you