l19 ch29 magnetic force · 2019. 8. 2. · the magnetic force on a moving charge after oersted’s...
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PHYS.1440Lecture19 A.DanylovDepartmentofPhysicsandAppliedPhysics
Lecture 19
Chapter 29
Magnetic Force
Physics II
Course website:https://sites.uml.edu/andriy-danylov/teaching/physics-ii/
PHYS.1440Lecture19 A.DanylovDepartmentofPhysicsandAppliedPhysics
Solenoid
Auniformmagneticfield canbegeneratedwithasolenoid.
AsolenoidisahelicalcoilofwirewiththesamecurrentIpassingthrougheachloopinthecoil.
PHYS.1440Lecture19 A.DanylovDepartmentofPhysicsandAppliedPhysics
Steps to make a solenoidMagneticfieldlinesproducedwithastraightwire
Let’sbendthewireintoaloop
Now,let’saddmoreloops
Auniformmagneticfieldisgeneratedwithasolenoid.
PHYS.1440Lecture19 A.DanylovDepartmentofPhysicsandAppliedPhysics
where n N/l is the number of turns per unit length.
Along the bottom (ab), the line integral is zero since B 0outside the solenoid.
Along the sides (bc, da), the line integral is zero since the field is perpendicular to the path.
dsB
B
B=0dsBds
∙abcda
0 0 0
0 ∥
There are N loops with current I enclosed by an Amperian loop, so ∙
∙ ∙ ∙ ∙
Uniform field
Amperian loopabcda
∙
/
Take-home quizExample The Magnetic Field
of a Solenoid
PHYS.1440Lecture19 A.DanylovDepartmentofPhysicsandAppliedPhysics
This patient is undergoing magneticresonance imaging (MRI). The large cylindersurrounding the patient contains a solenoidthat is wound with superconducting wire togenerate a strong uniform magnetic field.
B=1.2 T, I=100 A
Application of solenoids - MRI
PHYS.1440Lecture19 A.DanylovDepartmentofPhysicsandAppliedPhysics
Electromagnet• Themagneticfieldoutsideasolenoidlookslikethatofabarmagnet.• Thusasolenoidisanelectromagnet
FF
PHYS.1440Lecture19 A.DanylovDepartmentofPhysicsandAppliedPhysics
Electric Field Magnetic Field
From Coulomb’s law1
4̂
Biot-Savart law
4̂
Gauss’s Law
∙
Ampere’s Law
∙
So,nowweknowhowtofindmagneticfieldsusingBio‐SavartandAmpere’slaws.Now,thequestionis“howdoesamagneticfieldinteractwithmaterial(whichconsistsofchargesandcurrent)?”
Magnetic force on a moving charge
Magnetic force on current
PHYS.1440Lecture19 A.DanylovDepartmentofPhysicsandAppliedPhysics
Magnetic force on a moving charge
PHYS.1440Lecture19 A.DanylovDepartmentofPhysicsandAppliedPhysics
The Magnetic Force on a Moving Charge
AfterOersted’s discovery,thereweremanyotherexperimentswithmagneticfields,currents,charges,etc.ItwasfoundthatBexertsaforceonamovingcharge.
ThemagneticforceonachargeqasitmovesthroughamagneticfieldBwithvelocityv is:
where is the angle between v and B.
PHYS.1440Lecture19 A.DanylovDepartmentofPhysicsandAppliedPhysics
Let’s play with the Magnetic Force on a moving charge
A magnetic field has no effect on a charge moving parallel/antiparallel to the field
ConcepTest B field of q
A)TotherightB)TotheleftC)IntothescreenD)OutofthescreenE)Themagneticforceiszero
Thedirectionofthemagneticforceontheprotonis
ConcepTest B field of q
A)UpwardB)DownwardC)IntothescreenD)OutofthescreenE)Themagneticforceiszero
Thedirectionofthemagneticforceontheprotonis
PHYS.1440Lecture19 A.DanylovDepartmentofPhysicsandAppliedPhysics
Applications
PHYS.1440Lecture19 A.DanylovDepartmentofPhysicsandAppliedPhysics
Magnetic Force in “Art”
Nam June Paik’s Magnet TV (1965) at the truly amazing new Whitney Museum of American Art.
Magnet TV1965/99
Electrons in a kinescope are deflected by a
magnetic field
(a Korean‐American artist)Nam June Paik
PHYS.1440Lecture19 A.DanylovDepartmentofPhysicsandAppliedPhysics
Thank you
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