电磁场与电磁波（第三版）课后答案第5章

5.1

5.1

I

I

I

0

Be

z

2r

b

I

I

d

3b2

2

z

I

0

d

3b2

z

x

BdS

[dz]dx

dx

0

2

x

S

x

d

0

d

d

xd

3

5.1

z(xd)tan

S

6

d

3b2xd

I

Ibd

[

3

3b

)]

2d

5.1

0

dx

x

0

ln(1

3

2

d

5.2

5.2

J

B

J

J

J

b

a

J

Bdl

I

0

J

b

C

0

0

Jr

b

rb

2

b

r

b

r

a

B

a

b

b

2

d

Jr

b

J

rb

b

o

ob

2

r

a

2

b

b

a

J

5.2

0Jr

a

ra

a

2

B

a

a

2

Jr

a

ra

a

0

2

r

2

a

rr

ab

o

o

P

a

b

B

B

a

b

b

r

2

2

a

r

2

2

(rb)

b

B

0

J

r

b

r

a

2

b

a

a

r

2

2

B

0

J

r

b

r

a

(rb,ra)

2

b

a

a

(ra)

a

B

0

Jrr

ba

0

Jd

2

2

o

o

a

d

b

5.3

J

(1)

(2)

(3)

(4)

Hear,B

H

r

0

He(ay)eax,B

x

H

y

0

Heaxeay,B

H

x

y

0

Hear,B

H

0

B0

J

H

1

1

1

B

(rB)

r

(ar2)2a0

rr

rr

2

B

(ay)

(ax)0

y

x

e

e

e

x

y

z

J

H

e2a

z

x

y

z

ayax0

3

B

(ax)

(ay)0

y

x

eee

xy

z

J

H

0

xyz

axay0

B

1

1

4

B

(ar)0

rsin

rsin

erersine

r

1

J

H

eactag

r

e2a

r

2

sin

r

0

0arsin

2

J(r)

A(r)

d

5.4

4

R

J(r)R

d

R

3

B(r)

0

4

B0

:

J(r)

J(r)

d

R

B(r)

A(r)

0

d

0

4

R

4

1

J(r)

()d

0

4

R

R

J(r)R

d

R

3

J(r)(

)d

0

0

4

R

3

4

B

[

A(r)]0

5.5

J(r)erJ(ra)

0

A(r)

A(r)

B(r)

z

e

r

e

r

z

z

A(r)eA(r)

z

A(r)

z

z

A(r)

B(r)

A(r)

B(r)

rara

A(r)A(r)

2

ra

ra

1

1

A

)

r

2

2

A(r)

z1

(r

z1

Jr

0

0

rr

1

A

A(r)

z2

(r

z2)0

ra

rr

r

1

9

A(r)

z1

Jr3ClnrD

0

0

1

1

A(r)ClnrD

z22

2

A(r)A(r)

z1z2

r0

A(r)

z1

A

A

ra

A(a)A(a)

z1z2

z1

z2

r

a

r

a

r

r

1

9

1

3

1

C0

1

Ja

0

3

ClnaD

2

Ja

0

2

C

0

3

2

3

0

2

a

1

3

1

1

(

3

C

Ja

0

D

Ja

0

lna)

2

0

2

0

3

1

A(r)

z1

Jr

0

3

D

ra

0

1

9

1

1

3

1

3

A(r)

z2

Ja

0

3

lnr

Ja

0

3

(

lna)

ra

0

0

3

D

r0

A(r)0

z1

1

D0

1

z

P(x,y,z)

r

a

y

b

I

x

5.6

1

3

B(r)

1

A(r)e

1

Jr2

0

ra

0

Ja

0

3

ra

B(r)

2

A(r)e

2

0

3r

b

5.6

5.6

a

I

pr

m

1

P(x,y,z)

A(r)

A(r)

0

4r

3

p

eIab

z

m

2

A

B

B

I

abee

z

B

0

(d)

d

r

4

r

2

I1

1

A(r)

0

dl

4

R

C

R[(xx)

2

(yy)

dl

2

z

2

]

12

[r

2

2rsin

(xcos

ysin)x

2

y]

212

1

1

()

R

dS

dl

dS

R

C

S

C

S

1

()

R

1

()

R

I

1

()

A(r)

0

dS

4

R

S

r

x,r

y

Rr

I

1

()

r

1

()

r

1

()

r

A(r)

0

dS

0

[IdS]

0

(eIab)

z

4

4

4

4

S

S

r

pr

m

0

p(

m

)

0

r

3

4r3

r

psin

m

2

A(r)

pe(

z

)e

0

0

m

r3

r2

4

4

p

1

1

(e2cos

r

esin)

0

m

B

Ae

(sinA)e

(rA)

4

r3

r

rsin

rr

cos

ee

z

e2cos

r

esin

r

3

(

)

r

3

(

r)

r2

r2

p

ee

z

I

abee

z

I

0

B

0

m

(

)

0

(

)

(d)

r

r

4

r

2

4

r

2

4

5.7

a

M

e(Az2B)

z

AB

J

M

e

(Az2B)

ee2Az0

zz

m

z

M

(Az

2

B)

2Az

m

z

J

Mn

ee(Aa

z

2

cos

2

B)

z

mS

r

a

r

e(Aa

2

cos

2

B)sin

I

1

2

0

nM

ee(Aa

r

2

cos

2

B)

m

r

a

z

x

(Aa2cos2

I

B)cos

5.8

5.8

5.8

1

2

B

B

1

2

1

2

I

1

He

2r

I

B

B

He

0

1

2

0

2r

I

He

2r

2

1

(

)I

M

J

B

He

0

2

2

r

0

0

H(P)H(P)

1

1

2

1

1d

(

)I1d

rd

1

(r)0

r

l

Me

(rM)e

0

0

h

m

zrdr

z

2

H(P)H(P)

B

r0

r0

1

2

2

2

2

1

2

I

r

z

C

m

5.9

1

I

II

Bdl

m

0

C

0

I

(

1I)

m

0

(

)I

0

J=M?e

mS

e

r

zz=0

2

r

0

5.9

H

0

H

1

2

1

H

2

BB

1

B

2

H

H

H

1

2

0

5.9

2hl

HdlH(P)hH(P)hH(P)hH(P)

2

hI

1

1

2

1

1

2

2

C

1

Hl0

H

I

Hdl2H(P)h2H(P)hI

0

2

0

0

1

2

C

1

2

PP

1

H

H

2H

2

1

2

0

B

B

2H

0

1

2

2

B

H

1

2

0

1

2

B

B

2

2

H

H

H

H

2

1

1

0

2

0

1

1

2

2

1

2

5.10

A

n

B

A

BdS

AdS

Adl

A

1

S

S

C

1

l

P

P

h

5.10

C

l

h

C

1

C

h

A

2

AdlAlAllim

BdS

1

2

h

0

S

5.10

C

B

AlAl0

1

2

l

A

A

1t

2t

5.11

B

B

0

0

BH

B

1T

5000

0

0

M

H

H

1t

2t

HH

B

0

0

0

B

H

B

0

0

B

1

4999

M

H

(

1)B

0

0

0

0

0

B

B

1n

2n

BB

0

HB

B

0

B

1

1

)B

0

4999

M

H(

5000

0

0

0

512

5.12

15cm

r

0

a2cm

1

N1000

I0.7A

1400

r

2

3

l

0.1cm

0

r

1

a

r

0

NI

H

2r

0

a

2

N

2

I

r

NSH

a

0

2r

o

0

l

0

I

5.12

a

2

N

2

1400410

7

0.02

2

1000

2

L

2.346H

I

2r

20.15

0

2

B

B

B

0

H

H

0

HlH(2rl)NI

0

00

0

NI

r

B

H

B

H

B

0

B

B

B

0

0

r

0

0

0

l(2rl)

0

r0

0

a

2

N

2

I

NSB

0

r

l(2rl)

0

r0

0

aN

22

4

2

10

7

14000.02

2

1000

2

L

0

r

0.944H

I

l(2rl)

00

14000.0012

1

0.150.001

r0

3

W

HSl

2

m0

0

0

0

2

1

2

W

H2S(2rl)

m

0

r

0

0

W

W

l

r0

14000.001

20.150.001

1.487

m0

m

2rl

0

0

5.13

L1R

0

R

NI

NI

m

m

LN2R

W

R

m

2

2

m

m0

0

W

N

2

W

m

m0

I

LI

0

NI

I

0

R

m

NI

2

N

2

0

R

m

N

R

2

L

I

m

1

2

I

2

R

LI2

0

2

W

m

NI

m0

0

2R

2

m

1

N

2

I

2

NR

2

m

2

N2W

W

LI2

m

0

m0

2

2R

2

m

5.14

5.14

l

1

l

l

w

1

1

2

I

w

2

S

1

w

1

II

1

l

>>l

2

1

2

S

r

l

02ln

(Sw)(Sw)

2

w

2

M

1

2

S(Sww)

2

1

l

2

>>l

l

1

2

5.14

I

1

I1

1

B

(

)

rrw

0

1

12

2

1

12

S

w

I

1

1

Il

Sw

S

Sww

2

0

1

(

)ldr

0

12ln

2

ln

1

2

12

2

2

rrw

2

Sw

S

1

1

Illn(Sw)(Sw)

012

1

2

2

S(Sww)

12

l

02

(Sw)(Sw)

12

M

ln

12

1

I

2

S(Sww)

12

5.15

5.15(a)

a

R

M

ln

[2b(R2C2)12b2R2]12

0

2

b

A

B

A

B

a

R

R

1

R

C

b

C

P

Q

P

Q

5.15(a)

5.15(b)

I

I

B

0

2r

5.15(b)

R

I

aI11

aI

R

ln

1

R

BdS

dr

0

0

0

2

2

r

2

S

R

R[C2(b

R2C2)2]12[R2b22bR2C2]1