Chapter 19: Magnetic Fields - phys.ufl.edu Chapter 19 2 Magnetic Fields ÎMagnetic field (units,...

PHY2054: Chapter 19 1

Chapter 19: Magnetic Fields


Magnetic Fields Magnetic field (units, field lines)

Magnetic field of the earth and other astronomical objects

Effects of magnetic fields on charges and currentsForce on a moving chargeForce on a currentTorque on a current loopPath followed by particle in magnetic field

Generating magnetic fieldsLong wireCurrent loopSolenoid

InstrumentsMass spectrometersCyclotrons and synchrotrons


Reading QuizThe magnetic force on a moving charged particle is:

(1) Perpendicular to the velocity(2) Parallel to the velocity(3) Parallel to the B field(4) Independent of the velocity(5) None of the above


Reading QuizWhen I cut a magnet into two pieces I get:

An isolated north and south magnetic poleTwo smaller magnetsThe two pieces are no longer magnets


Reading QuizConsider +q moving relative to a B field as shown. What is the direction of the magnetic force?

Force is parallel to vForce is parallel to BForce is into the pageForce is out of the page B

+q

PHY2054: Chapter 19 7Fig. 19-1, p.625


Bar MagnetsTwo poles: “north” and “south”

Like poles repel

Unlike poles attract

Magnetic poles cannot be isolated

NS

Similar to dipole field from electrostatics


Interaction of Magnetic Poles

N – SAttract

N – NRepel

1 magnet


Magnetic Monopoles?Can any isolated magnetic charge exist?

We would call this a “magnetic monopole”It would have a + or – magnetic charge

How can we isolate this magnetic charge?Cut a bar magnet in half? NO!

Magnetic monopoles have never been seen!

What you getis a bunch oflittle magnets!


Searches for Magnetic Monopoles


Earth is a big magnet!!

The North pole of a small magnet (compass) points towards geographic North because Earth’s magnetic South pole is up there!!

Particles moving along field lines cause Aurora Borealis.http://science.nasa.gov/spaceweather/aurora/gallery_01oct03.html

PHY2054: Chapter 19 13Fig. 19-4, p.626


What Causes Magnetism?What is the origin of magnetic fields?

Electric charge in motion!For example, a current in a wire loop produces a field very similar to that of a bar magnet (as we shall see).

Understanding the source of bar magnet field lies in understanding currents at the atomic level within matter

Orbits of electrons about nuclei

Intrinsic “spin” of electrons (more important effect)


Magnetic Field UnitsFrom the expression for force on a current-carrying wire:

B = Fmax / I LUnits: Newtons/A⋅m ≡ Tesla (SI unit)Another unit: 1 gauss = 10-4 Tesla

Some sample magnetic field strengths:Earth: B = 0.5 gauss = 0.5 x 10-4 TGalaxy: B ∼ 10-6 gauss = 10-10 TBar magnet: B ∼ 100 – 200 gaussStrong electromagnet: B = 2 TSuperconducting magnet: B = 5 – 10 TPulse magnet: B ∼ 100 TNeutron star: B ∼ 108 – 109 TMagnetar: B ∼ 1011 T


PulsarsRapidly Rotating Neutron Stars

Enormous Magnetic Fields

Beam off Beam on

Crab PulsarR = 10 kmM = 1.4 solar massB ≈ 108 TPeriod = 1/30 sec


Magnetic Force on Moving ChargeMagnetic force acts only on moving charge

Force direction is perpendicular to both B and vRight hand rule (next slide)

Force direction depends on sign of chargeForce is in opposite direction from positive charge

Force magnitude depends on direction of v relative to Bv is parallel to B ⇒ sinφ = 0v is perpendicular to B ⇒ sinφ = 1v is at angle 45° to B ⇒ sinφ = 0.71

sinF qvB φ=

F qvB=0F =

sin 45F qvB=


Direction of Magnetic Force

F perpendicular to v and B


Right Hand Rule For Magnetic ForceFirst point fingers in direction of velocity

Curl fingers toward B field⇒ Thumb points toward force

F

v

B

B

+q

v

F is into page


ExampleParticle with m = 2.0 g, q = −2μC moves with v = 2,000 m/s through B field of 2.5 T at an angle of 30° to the field.

Magnitude of force

Direction of force: up out of the page. Use RHR and take opposite direction because of −q

B

−q

v

F is up out of page

( )( )( )( )6

2

sin 2 10 2000 2.5 0.5 0.005N

/ 0.005/ 0.002 2.5m/s

F qvB

a F m

φ −= = × =

= = =


QuizA charged particle moves in a straight line through some region of space. Can you conclude that B = 0 here?

(1) Yes(2) No

A B field can exist since if v || Bthere is no magnetic force


A negative particle enters a magnetic field region. What path will it follow?

(1) A(2) B(3) C(4) D(5) E

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 xx x x x x x x x x x x x

Magnetic Force

AB

C

D

E

(1) RHR says it bends down (− charge)(2) But force cannot instantaneously change v

and the velocity vector bends continuously(3) So the answer is D, not E


Magnetic Force on Current-Carrying WireMagnitude of force on current

Direction of force: RHR

( ) ( )( ) ( ) ( )force on one charge # of charges

sin sin sind e e d

F

ev B n AL en v A BL iBLφ φ φ

= ×

= × = =

=i


F

F


ExampleA 4 m long wire carries current of 500A in NE direction

Magnitude of force (B = 0.5 gauss = 5 × 10-5 T, pointing N)φ = 45°

Direction of force: Upwards, from RHR

Can adjust current in wire to balance against gravityCalculate mass from density, length and cross-sectional area

siniBL mgφ =

( )( )( )( )5sin 45 500 5 10 4 0.71 0.071NF iBL −= ° = × =

density volumem LAρ= = ×

sinAgi

Bρ

φ=

Chapter 19: Magnetic Fields - phys.ufl.edu Chapter 19 2 Magnetic Fields ÎMagnetic field (units,...

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