Solenoid1.长直螺线管内的磁感应强度CAI

We assume that the length of the solenoidis much greater than the diameter

Magnetic field lines for a real solenoid of finite length. The field is strong and uniform at interior points such as P1 but relatively weak at external points such as P2.

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∫∫ ∫∫ ∫ ⋅+⋅+⋅+⋅=⋅a

d

c

b

d

cL

b

aldBldBldBldBldBvvvvvvvvvv

0=⋅=⋅ ∫∫a

d

c

bldBldBvvvv

CAI

∫ =⋅d

cldB 0vv

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hBldBldBb

aL⋅=⋅=⋅ ∫∫

vvvv

The rectangular loop encloses the current：

hniI i ⋅⋅=∑ioL

IldB ∑=⋅∫ µvv

hnihB o ⋅⋅=⋅ µ

niB oµ=

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2. 无限大平面电流的磁场An infinite slab carries a uniform current

αSurface current density

lI

∆∆α =

1011 lBlBl αµ=+ 20αµ=B

l∆I∆α

10 lαµ=

面电流密度

a b

cd

1l

2l

Br

Br

∫∫∫ ⋅+⋅=⋅c

b

b

aLldBldBldBrrrrrr

∫∫ ⋅+⋅+a

d

d

cldBldBrrrr

∫∫ ⋅+⋅=d

c

b

aldBldBrrrr

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Bd ′r

Bdr 2Bdr

1Bdr

The magnetic field produced by a moving charged particle

nvq r qnvSI =

ld//vqrr

30

4 rrlIdBdrr

r ×=

πµ

载流子

SdlvqnlIdrr

=

of carrieres charge by produced is The nSdldNBd =r

lqnvSdlIdrr

=

30

4 rrvqnSdl rr

×=

πµ

30

4 rrvq

dNBdB

rrrr ×

==πµ

A charge carriercv <<

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30

4 rrvqBrrr ×

=πµ载流子

A charge carrier

Br

rr

vrq + B

r

rr

vrq−

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§9.4 带电粒子在磁场中的运动The Motion of a Charged Particle in a Magnetic Field

(1) A charged particle moves parallel to a constant magnetic field

BvqFrrr

×=

+q

Br

vr

θsinqvBF =

0=θ

0=F

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(2) A charged particle moves perpendicularly to a constant magnetic field

+q

Br

vr

Fr

RR

×× ×× ×× ×× ×× ×× ××

×× ×× ×× ×× ×× ×× ××

×× ×× ×× ×× ×× ×× ××

×× ×× ×× ×× ×× ×× ××

×× ×× ×× ×× ×× ×× ××

×× ×× ×× ×× ×× ×× ××

++

Br

vr

Fr

BvqFrrr

×= qvB=θsinBqvF =

RvmqvB

2

=qBmvR =

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qBmvR =

qBm

vRT ππ 22==周期

mqThe period

mqB

Tf

π21==频率 荷质比

The frequency charge-to-mass ratio

The period and frequency are independent of the speed.

All particles with the same charge-to-mass ratio take the same time T (the period) to complete one round trip.

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(3)Initial velocity is not perpendicular to magnetic field

The particle will move in a helical path about the direction of the field vector 螺旋运动

h

⊥v

//v++ θ

Br

vrθcosvv // =

θsinvv =⊥

pitch of the helix 螺距

匀速圆周运动

匀速直线运动

the distance between adjacent turns

The velocity vector of such a particle resolved into two components, one parallel to and one perpendicular to it.

vr

Br

⊥v//v CAI返回 退出

h

⊥v

//v++ θ

Br

vrmove in a helical path

螺旋运动

pitch of the helix 螺距

qBmT π2

=

θπ cos2 vqB

mTvh // ==

The parallel component determines the pitch h of the helix

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Magnetic focusing 磁聚焦 从磁场某点发射出一束带电粒子流

⊥v

//v

vr

Brθ++

vqB

mvqB

mh πθπ 2cos2==vvv ≈= θcos//

θθ vvv ≈=⊥ sin

2RS π= CAIqfI =Magnetic mirror 磁镜

mqBfπ2

=qB

mvR ⊥=2qfRISM π==

B

mvM

2

21

⊥

=

const.=M

222

21

21

21

//mvmvmv += ⊥

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A charged particle spiraling in a nonuniform magnetic field. (The particle can become trapped, spiraling back and forth between the strong field regions at either end.) Note that the magnetic force vectors at the left and right sides have a component pointing toward the center of the figure.

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闭合环形结构

托卡马克

全超导非圆截面的托卡马克核聚变实验装置(EAST)

2006年9月28日成功实现首次物理放电实验返回 退出

范·阿仑（Van Allen）辐射带

1958年

⋅

探索者1号卫星

赤道上空3000km

赤道上空15000km

宇宙线、太阳风

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在美国国家航空航天局2003年10月28日公布的太阳表面图像上，可以清晰地观测到太阳表面聚集的由巨大黑子群释放出的冠状云。

体积约为地球13倍的巨型带电微粒云团自莫斯科时间2003年10月28日14时整开始从太阳表面喷发出来，并且以超过每小时150万千米的速度向地球靠近。

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太阳风

从太阳表面喷发出来的体积约为地球13倍的巨型带电微粒云团

高温和高速的质子流和电子流

像是一个无限大的导体靠近地球太阳风的导电性极好

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The auroral oval surrounding Earth's geomagnetic north pole. Magnetic field lines converge toward that pole. Electrons moving toward Earth are “caught by” and spiral around these field lines, entering the terrestrial atmosphere at high latitudes and producing aurora within the oval.

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太阳风暴光临地球引起地球两极出现壮丽的极光景观

aurora

美国阿拉斯加州安克雷奇的东北部山脉上空出现美丽的极光

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太阳风暴光临地球引起地球两极出现壮丽的极光景观

aurora

美国阿拉斯加州安克雷奇的东北部山脉上空出现美丽的极光

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