8 磁場

How is an aurora so thin yet so tall and wide?

Introduction

How does magnetic resonance imaging (MRI) allow us to see details in soft nonmagnetic tissue?

How can magnetic forces, which act only on moving charges, explain the behavior of a compass needle?

The magnetic field

The electric field and the magnetic field

Electromagnets and permanent magnets

8-1 The definition of B

BvqFB

m)(V (N/C)

0

q

FE

The tracks in a bubble chamber

Figure 27.21

The SI unit for B

1 tesla = 1T =1 N/A‧m=104 gauss

108 T

1.5 T

10-2 T

10-4 T

10-10 T

10-14 T

Magnetic Field Lines Magnetic vs. electric dipoles

A horseshoe and a C-shaped magnets

例 1 A 5.3 MeV proton

7

15

12 2

2 / 3.2 10 m/s

sin 6.1 10 N

/ 3.7 10 m/s

B

B

v K m

F qvB

a F m

B = 1.2 mT

8-2 Crossed Fields: Discovery of the Electron

A cathode ray tube

Thomson’s procedure:

設定E = 0 、 B = 0 ，並記錄光點位置

開啟電場、測光點偏移量

開啟磁場，並調整其值，直至光點回復未偏移位置

2

2

2 2

, 2

/ , 2

qELy qE qvB

mv

m B Lv E B

q yE

Calculation

2

2

2

2

,2

1

x

xy

y

mv

QELy

tvLtay

m

QE

m

Fa

the charge-to-mass ratio of

the electron ：

1.75881961011 C·kg-1

8-3 Crossed Fields: The Hall Effect

By the conduction electrons in copper:

)(

d

Al

Vle

Bin

neA

i

ne

Jv

BeveE

EdV

d

d

例 2 A cube generator

mV0.3

V

dvBV

EdV

evBeE

d = 1.5 cm, v = 4.0m/s, B = 0.05T

8-4 A Circulating Charged Particle

qBm

vrT

qBmvr

rmvqvB

rmvmaF

/2

/2

/

/

/

2

2

Figure 27.17a

Figure 27.17b

The frequency and angular frequency

2 2

1

m

qBf

m

qB

Tf

頻率與軌跡

The magnetic bottle machine

Helical Paths

2cos

mp v T v

qB

The pitch (螺距) of the helical path

cos sinv v v v

V∥ and V⊥

極光橢圓圈

例 3 The Mass Spectrometer (質譜儀)

2

21

/2

2

1 2

rx

q

mV

BqB

mvr

mqVv

qVmv

u93.2038

222

22

V

qxBm

q

mV

Brx

Isotope Separation

Centrifuge and diffusion chamber

質譜儀 x = 1.6254m, V = 1000.0V, B = 80.000mT

8-5 Cyclotrons and Synchrotrons

Fermilab: 6.3km ring

(迴旋加速器與同步加速器)

The resonance condition:

When proton energy > 50Mev:

Out of resonance (relativistic effect)

A huge magnet (4×106 m2) is needed for high energy (500Gev) protons

The proton sychrotron at Fermilab can produces 1Tev proton

oscff Synchrotrons

CERN LHC

The LHC is 27km long and sits 100m below the surface.

Large Hadron Collider

• Baryon

fermion

• Meson

boson

8-6 Magnetic Force on a Current-Carrying Wire

BLiF

iLBBqvF

viLitq

B

dB

d

sin

/

For a wire segment:

BLidFd B

Magnetic Force

例 4 A length of wire with a semicircular arc

)(2

2cos

sinsin

)(

321

0

0 02

31

RLiBFFFF

iBRiBR

diBRdFF

RdiBiBdLdF

iLBFF

Calculation

線圈

8-7 Torque on A Current Loop

F2 and F4 cancel

F1 and F3 form a force couple

sin)(

sin

)sin2

()sin2

(

cos)90sin(2

BNiAN

iabB

biaB

biaB

ibBibBF

N turns coil

例 5 A galvanometer for analog meters

degree/mM102.5

28/)]90)(sinT23.0(

)m1052.2)(A10250)(100[(

sin

sin

8

24-6-

NiAB

NiAB

The direct-current motor

Figure 27.40

8-8 The Magnetic Dipole

The magnetic dipole moments

The magnetic potential energy

) :cf(

sin

EpB

BNiA

)()( BUEpU

B

BBU

2

)()(

磁能