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