Лекции матмод

z

M r,), z

ez

e)

z

er

k

j

O

r

y

i

)

Ez

2

E2z

2

E2z

2

E2z

Ez

Ez

1

r

1

1

b

2

2

r r

r

r

)

z

a

t

t

1

Ez (t, r)

1 2Ez (t, r)

Ez

(t, r)

r

2

b

.

r

a

2

t

t

r r

jz (t, r)

1

Ez (t, r)

Re j(r)ei?t ,

6

6

1

1 2

Re j(r)ei?t

Re j(r)ei?t

Re j(r)ei?t

r

b

.

r

r

a2

t2

r

t

1 d

d j(r)

?2

r

j

(r)

a

2

i?b

r d r

d r

1

d

d

2

.

d.

j

(. )

h

j(. ) 0 ,

(109)

.

d.

r

j(. r )

j0

I

? 2

:

0

.

r

; j(. )

j

;

$ r2

; h r:

a2 i?b .

:

0

:

& B ( -

" )

x2

d 2 y

x

d y

x2 n2

y 0,

2

dx

dx

'

.

j(. )

. 9 C1

r:

I(t) Re I ei?t

@2$ r Re j(r)ei?t d r .

0

*

r:

r: r j(r) dr

1

I

@2$ r j(r)d r 2I0 @

2I0

@. C1 J0 (h. )d.

r

j

r

0

0 :

0

:

0

2C1 I0

h

2C1 I0

'xJ1(x)(

h

2C1 I

0 J1

(h)

@ xJ0 (x)d x

,

h

2

h

2

0

h

0

J1 — " B . * ,

d

xn Jn (x) xn Jn 1(x) ,

dx

d

x J1(x) x J0 (x) .

dx

t

2C1 I0

J1(h)

I I0

.

h

* ,

C1

h

.

2J1 (h)

J

0

hr / r

jz (t, r)

Re

j(r)ei?t

j0

Re

h

:

ei?t .

J1(h)

2

? 1 0 h r:

?2 / a2 i?b 1 0 , ,

J0 hr / r: 1 1

h2

1 2 .

h J1(h)

$

lim j

(t, r) j .

?1 0 z

0

jz (t, r) Re j(r)e

i?t

#

j0 Re " Re j(r / r: ) i Im j(r / r: ) cos?t i sin?t

j0 Re j(r / r: )cos?t Im j(r / r: )sin?t A(r / r: )sin ?t ) ,

2

2

j0

—

A(r / r:) j0 Re j(r / r:)

Im j(r / r: )

j(r / r:)

; ?t ) — " ,

) arctg

.

Im j(r / r: )

W

A02

l

,

S6

2

R

l

l

.

S6

$ r2

6

0

:

A02

l

2$ r r A 2

l

$ r l 2

W

2

6

A

2

2$ r r 6

2$ r r 6

r

r:

$ r l

'A(r / r: )(

2

$ l

r:

2

2

W @

dr

@

6

6

j0

j(r / r: )

r dr

0

0

I

2

$ r:2 j0

2

W

0

R

R ,

2

2

2$

@ H dl

@ H) (t, r)dl @ H) (t, r)r d) 2$ rH) (t, r) I ,

L

L

0

r

2$ rH) (t, r) I @2$ jz (t,2)2 d2

0

,

1 r

1 r

I

I

H) (t, r)

@0

jz (t,2)2 d2

@0

2 d2

r ,

r

r

$ r:2

2$ r:2

e

1

BH

1

B2

1

3

3 H 2

,

303

m

2

2

2

0

E

@@@V

303 H 2 d

@@@V

303 H 2 r dr d) dz

1

2

)

2

)

r*

303

I

2

303 l

2 r*

3

303 l

2

2$ l@

2

r r dr

4$ r4

I

@r

d r

16$

I

,

2$ r2

0

*

*

0

z

M r,), z

l/2

303c I

ds

dB

4$ 3

d s Q

z

O

s

r

y

)

x

I

–l/2