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# 10 電磁 III - PowerPoint PPT Presentation

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

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

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 vs. electric dipoles

1 A 5.3 MeV proton

B = 1.2 mT

• 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

the charge-to-mass ratio of the electron

1.75881961011 C·kg-1

• By the conduction electrons in copper:

2 A cube generator

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

10-1.4A Circulating Charged Particle

The frequency and angular frequency

The magnetic bottle machine

V∥ and V⊥

The pitch (螺距) of the helical path

3 The Mass Spectrometer (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

• 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

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

10-1.6Magnetic Force on a Current-Carrying Wire

For a wire segment:

4 A length of wire with a semicircular arc

10-1.7Torque on A Current Loop

• F2 and F4 cancel

• F1 and F3 form a force couple

5 A galvanometer for analog meters

10-1.8The Magnetic Dipole

• The magnetic dipole moments

• The magnetic potential energy

Conventional rocket EM Rail Gun

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

6 What B does the current produce?

7 The Field Between Two wires

• 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

7 A hollow conducting cylinder

• Magnetic Field of a Solenoid (螺線管)

• Magnetic Field of a Toroid (螺線環)

Tokamak Fusion Test Reactor

• A current loop and a bar magnet

• 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

• Flux  enclosed charge

• From G.L. to C.L.