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PHYS.1440 Lecture 20 A.Danylov Department of Physics and Applied Physics 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/

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Page 1: L20 Ch29 Cyclotron Motion · The Cyclotron The first practical particle accelerator, invented in the 1930s, was the cyclotron. Cyclotrons remain important for many applications of

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/

Page 2: L20 Ch29 Cyclotron Motion · The Cyclotron The first practical particle accelerator, invented in the 1930s, was the cyclotron. Cyclotrons remain important for many applications of

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

Page 3: L20 Ch29 Cyclotron Motion · The Cyclotron The first practical particle accelerator, invented in the 1930s, was the cyclotron. Cyclotrons remain important for many applications of

PHYS.1440Lecture20 A.DanylovDepartmentofPhysicsandAppliedPhysics

Cyclotron Motion

Manyimportantapplicationsofmagnetisminvolvethemotionofchargedparticlesinaperpendicularmagneticfield

There is an amazingly beautiful application of 

Page 4: L20 Ch29 Cyclotron Motion · The Cyclotron The first practical particle accelerator, invented in the 1930s, was the cyclotron. Cyclotrons remain important for many applications of

PHYS.1440Lecture20 A.DanylovDepartmentofPhysicsandAppliedPhysics

Cyclotron motion

Thefigureshowsapositivechargemovinginaplanethatisperpendiculartoauniformmagneticfield.

B into page

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

Thismotioniscalledthecyclotronmotionofachargedparticleinamagneticfield.

Page 5: L20 Ch29 Cyclotron Motion · The Cyclotron The first practical particle accelerator, invented in the 1930s, was the cyclotron. Cyclotrons remain important for many applications of

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

Page 6: L20 Ch29 Cyclotron Motion · The Cyclotron The first practical particle accelerator, invented in the 1930s, was the cyclotron. Cyclotrons remain important for many applications of

PHYS.1440Lecture20 A.DanylovDepartmentofPhysicsandAppliedPhysics

Cyclotron motion (general situation)

B

∥

Thefigureshowsamoregeneralsituationinwhichthechargedparticle’svelocityisnotexactlyperpendiculartoB.

Thecomponentof v paralleltoBisnotaffectedbythefield,sothechargedparticlespiralsaroundthemagneticfieldlinesinahelicaltrajectory.

Theradiusofthehelixisdeterminedbyv,thecomponentofvperpendiculartoB.

Page 7: L20 Ch29 Cyclotron Motion · The Cyclotron The first practical particle accelerator, invented in the 1930s, was the cyclotron. Cyclotrons remain important for many applications of

PHYS.1440Lecture20 A.DanylovDepartmentofPhysicsandAppliedPhysics

Aurora (Northern lights)

Charged particles(solar wind)

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

Page 8: L20 Ch29 Cyclotron Motion · The Cyclotron The first practical particle accelerator, invented in the 1930s, was the cyclotron. Cyclotrons remain important for many applications of

PHYS.1440Lecture20 A.DanylovDepartmentofPhysicsandAppliedPhysics

The Cyclotron

Thefirstpracticalparticleaccelerator,inventedinthe1930s,wasthecyclotron.

Cyclotronsremainimportantformanyapplicationsofnuclearphysics,suchasthecreationofradioisotopesformedicine.

Page 9: L20 Ch29 Cyclotron Motion · The Cyclotron The first practical particle accelerator, invented in the 1930s, was the cyclotron. Cyclotrons remain important for many applications of

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)

, , ,

Page 10: L20 Ch29 Cyclotron Motion · The Cyclotron The first practical particle accelerator, invented in the 1930s, was the cyclotron. Cyclotrons remain important for many applications of

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.

Page 11: L20 Ch29 Cyclotron Motion · The Cyclotron The first practical particle accelerator, invented in the 1930s, was the cyclotron. Cyclotrons remain important for many applications of

PHYS.1440Lecture20 A.DanylovDepartmentofPhysicsandAppliedPhysics

Magnetic force on Current-Carrying Wires

Page 12: L20 Ch29 Cyclotron Motion · The Cyclotron The first practical particle accelerator, invented in the 1930s, was the cyclotron. Cyclotrons remain important for many applications of

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

Page 13: L20 Ch29 Cyclotron Motion · The Cyclotron The first practical particle accelerator, invented in the 1930s, was the cyclotron. Cyclotrons remain important for many applications of

PHYS.1440Lecture20 A.DanylovDepartmentofPhysicsandAppliedPhysics

There’snoforceonacurrent‐carryingwireparalleltoamagneticfield.

Magnetic Forces on Current-Carrying Wires

∥

Page 14: L20 Ch29 Cyclotron Motion · The Cyclotron The first practical particle accelerator, invented in the 1930s, was the cyclotron. Cyclotrons remain important for many applications of

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

Page 15: L20 Ch29 Cyclotron Motion · The Cyclotron The first practical particle accelerator, invented in the 1930s, was the cyclotron. Cyclotrons remain important for many applications of

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

Page 16: L20 Ch29 Cyclotron Motion · The Cyclotron The first practical particle accelerator, invented in the 1930s, was the cyclotron. Cyclotrons remain important for many applications of

PHYS.1440Lecture20 A.DanylovDepartmentofPhysicsandAppliedPhysics Slide 32-147

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

Page 17: L20 Ch29 Cyclotron Motion · The Cyclotron The first practical particle accelerator, invented in the 1930s, was the cyclotron. Cyclotrons remain important for many applications of

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:

Page 18: L20 Ch29 Cyclotron Motion · The Cyclotron The first practical particle accelerator, invented in the 1930s, was the cyclotron. Cyclotrons remain important for many applications of

PHYS.1440Lecture20 A.DanylovDepartmentofPhysicsandAppliedPhysics

Thank you


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