Elect Magnet 11

8/2/2019 Elect Magnet 11

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11 11


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8. 8.

8.1. 8.1.

8.2. 8.2. --

8.3. 8.3.

8.4. 8.4.

8.5. 8.5.

8.6. 8.6.

8.7. 8.7.


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8.4. 8.4.

B, dsB, ds .. BB-- : : B=B=mm00I/2I/2ppaa

--

BB--

II BB

B ds

I

a

B ds Bds

B ds

00

I B ds B ds ( 2 a ) I

2 a

mp m

p

ds 2 ap

B


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--

mm00II-- , , , , BB

II--

:: IIkk

, ,

II11, I, I33 , , II22 I=0I=0

B ds

0 B ds I m

kI I

B ds 0

I1I2 I3


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BB

BB BB


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8.5 8.5 A long, straight wire of radiusA long, straight wire of radius aa carriescarries

a steady currenta steady current II00 that is uniformlythat is uniformly

distributed through the cross section ofdistributed through the cross section ofthe wire. Calculate the magnetic fieldthe wire. Calculate the magnetic fieldat a distanceat a distance rrfrom the center of thefrom the center of thewire in the regionswire in the regions rraa andand r


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11

((rraa ))

27.1 27.1-- , ,

r


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11 22

((r


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88.6.6

. . NN . . rr

. . ::

-- rr

The magnetic field of a toroidal coil:The magnetic field of a toroidal coil:The toroidal coil consists ofThe toroidal coil consists ofNNturns ofturns ofwire wrapped around a doughnutwire wrapped around a doughnutshaped structure as in Fig. Assumingshaped structure as in Fig. Assumingthat the turns are closely spaced,that the turns are closely spaced,calculate the magnetic field inside thecalculate the magnetic field inside thecoil, a distancecoil, a distance rrfrom the center.from the center.

B ds

r


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II mm00NINI

BB 1/r1/r-- r>>ar>>a

00 00

NN

B ds B ds

0 B ds B ds B( 2 r ) NI p m

0NIB2 r

m

p

r

2a


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88.7.7

. . yzyz jjss .. yy

jjss zz . .

. . ::

BB

, , BB

l, wl, w ll ,, ww


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, ,

jjssll

ww

0 s2Bl j l m s

0

jB

2

m


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8.5. 8.5.

2 2

,,

dAdA BB dAdA-- . .

AA , , BB ddAA-- qq

q=90 q=0 BA

mB dA

B dA

m BAcos q

, : 1=12


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::

BB-- , ,

, ,

: :

: : B dA 0


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88.8.8

BB dAdA dAdA ddmm=BdA=BdA

BB , , rr-- BB

dA=bdrdA=bdr . .

aa ,, bb II cc . .

. . . . ::

0IB2 r

m

p

0m

I BdA dA

2 r

m

p

a c a c0 0 0m cc

I Ib Ibdr a cb ln r ln

2 r 2 2 c

m m m

p p p


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8.6. 8.6.

PP

: :

SS


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: :

NN, , SS


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22 44 : : BB dsds ll 11 BlBl : : BB dsds--

II

ll,, ww

-- 33 B=0B=0

B ds


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ll NN

NINI

n=N/ln=N/l

. ? . ?

1 1 B ds B ds B ds Bl

0 B ds Bl NI m

0 0

N B I nI

lm m 0

NIB

2 r

m

p


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dxdx (N/l)dx(N/l)dx I(N/l)dxI(N/l)dx dxdx PP

x=Rtanx=Rtanff dx=Rsecdx=Rsec22ffddff

ll,, RR ,, NN , , II

PP

2

0x 3

2 2 2

IRB

2( x R )

m

2

0

32 2 2

R NdB I dx

l2( x R )

m


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xx ff ff11-- ff22

PP RR-- ff22=90=90,, ff11==--9090

PP

ff22 9090,, ff11 00

xx--

2

1

0 02 1

NI NI B cos d (sin sin )2l 2l

f

fm mf f f f

0 00

NI NI B ( 1 1 ) nI 2l l

m mm

01 B nI 2

m

8 7 8 7


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8.7. 8.7.

QQ

II . :. :

::

0 B ds I m

I dQ / dt


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SS22--

,, SS22

PP SS11 SS22

PP SS11 II mm00II

ed 0

dI

dt

e

E dA


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, , BB......

--

e0 d 0 0 0

d B ds ( I I ) I

dt

m m m

e E dA EA

0 0 E, A ? E / Q / A

e

0

QEA

ed 0

d dQI

dt dt

88 99


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88..99 8 8 3 3

30 30

. . :: ww=2=2pp f=2f=2pp(3(3101033)=6)=6pp101033 cc--11

V=VV=Vmmsinsinwwt=30sin(6t=30sin(6pp1010

33t) Bt) B

4,52 4,52

6 3

d

dQ d( CV ) dV d I C ( 8 10 ) 30 sin( 6 10 t )

dt dt dt dt p

34,52cos(6 10 t ) Ap

Elect Magnet 11

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