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
7-2 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
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
7-3 Crossed Fields: The Hall Effect
By the conduction electrons in copper:
)(
d
Al
Vle
Bin
neA
i
ne
Jv
BeveE
EdV
d
d
The frequency and angular frequency
2 2
1
m
qBf
m
qB
Tf
頻率與軌跡
The magnetic bottle machine
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
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
7-7 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
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
7-8 The Magnetic DipoleThe magnetic dipole moments
The magnetic potential energy
) :cf(
sin
EpB
BNiA
)()( BUEpU