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