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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?


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

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

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


10-1.4A Circulating Charged Particle


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


極光橢圓圈


例 3 The Mass Spectrometer (質譜儀)


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.


10-1.6Magnetic Force on a Current-Carrying Wire


Magnetic Force

For a wire segment:


例 4 A length of wire with a semicircular arc


Calculation


線圈


10-1.7Torque on A Current Loop

  • F2 and F4 cancel

  • F1 and F3 form a force couple


例 5 A galvanometer for analog meters


10-1.8The Magnetic Dipole

  • The magnetic dipole moments

  • The magnetic potential energy


磁能


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


Magnetic Field Due to a Current in a Long Straight Wire


Integration


Magnetic Field Due to a Current in a Circular Arc of Wire


例 6 What B does the current produce?


10-2.2 Two Parallel Currents


例 7 The Field Between Two wires


10-2.3 Ampere’s Law

  • Comparing Gauss’ law and Ampere’s law

  • Ampere’s law


The Magnetic Field Outside a Long Straight Wire with Current


The Magnetic Field Inside a Long Straight Wire with Current


例 7 A hollow conducting cylinder


10-2.4 Solenoids and Toroids

  • Magnetic Field of a Solenoid (螺線管)

  • Magnetic Field of a Toroid (螺線環)


Magnetic Field of a Solenoid


Magnetic Field of a Toroid


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


Magnetic Field of a Coil


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.


敬請期待電磁 IV


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