# 10 電磁 III - PowerPoint PPT Presentation

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10 電磁 III. How is an aurora so thin yet so tall and wide?. Sections. 磁場 電流與磁場. 10-1 磁場. The electric field and the magnetic field Electromagnets and permanent magnets. 10-1.1 The definition of B. The tracks in a bubble chamber. The SI unit for B.

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10 電磁 III

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## 10 電磁 III

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

• 磁場

• 電流與磁場

### 10-1 磁場

• The electric field and the magnetic field

• Electromagnets and permanent magnets

### 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

B = 1.2 mT

### 10-1.2 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

• 開啟磁場,並調至與電場相等

### Calculation

the charge-to-mass ratio of the electron

1.75881961011 C·kg-1

### 10-1.3 Crossed Fields: The Hall Effect

• By the conduction electrons in copper:

### 例 2 A cube generator

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

### 頻率與軌跡

The frequency and angular frequency

The magnetic bottle machine

### Helical Paths

V∥ and V⊥

The pitch (螺距) of the helical path

### 質譜儀

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

Isotope Separation

Centrifuge and diffusion chamber

### 10-1.5Cyclotrons and Synchrotrons

(迴旋加速器與同步加速器)

Fermilab: 6.3km ring

### Synchrotrons

• 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

### CERN LHC

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

### Magnetic Force

For a wire segment:

### 10-1.7Torque on A Current Loop

• F2 and F4 cancel

• F1 and F3 form a force couple

### 10-1.8The Magnetic Dipole

• The magnetic dipole moments

• The magnetic potential energy

### 10-2 Magnetic Fields due to Currents

Conventional rocket EM Rail Gun

1

dq

=

dE

pe

2

4

r

0

v

1

dq

v

=

d

E

r

pe

3

4

r

0

m

q

ids

sin

=

0

dB

p

2

4

r

v

v

m

id

s

r

=

0

dB

p

3

4

r

### 10-2.1 Calculating the Magnetic Field due to a current

The law of Biot and Savart

### 10-2.3 Ampere’s Law

• Comparing Gauss’ law and Ampere’s law

• Ampere’s law

### 10-2.4 Solenoids and Toroids

• Magnetic Field of a Solenoid (螺線管)

• Magnetic Field of a Toroid (螺線環)

### 磁圍阻核融合反應器

Tokamak Fusion Test Reactor

### 10-2.5 A Current Carrying Coil as a Magnetic Dipole

• A current loop and a bar magnet

### Coulomb’s Law

• Using Gauss’s law to take advantage of special symmetry situations

• Gaussian surfaces

• 高斯面上各點電場與面內總電荷相關

### Gauss’ Law

• Flux  enclosed charge

### Gauss’Law and Coulomb’Law

• From G.L. to C.L.