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14-1

14-2

14-3

14-4

14-5

14-6

14-7

14-8

14-9

14-10

14-1 试证明平行板电容器中的位移电流

d

U

I

=

C

d

t

d

d

U

l

Id

C

=

=

D

d

t

r

p

2

δ

δ

l

d

d

1

d

δ

e

e

=

r

2

p

d

U

d

t

0

0

Φ

=

S

d

d

Φ

d

U

C

C

C

Φ

U

=

=

=

d

t

d

t

d

D

=

d

t

σ

d

σ

=

=

D

d

t

14-2 在一对巨大的圆形极板(电容C=l.0

×10-12 F)上，加上频率为50Hz、峰值为

174000V的交变电压，计算极板间位移电

Um =1.74×105V 求：Idm

ω

Idm

=

C

Um

p

2

=

C

Um

f

e

e

0

0

Φ

d

Id

=

t

d

S

ω

Φ

cos

t

E

S

=

=

Um

d

S

C

=

d

ω

ω

sin

t

Id

=

C

Um

Id 的最大值

=1.0×10-12×2p×50×1.74×105

=5.74×10-5(A)

d

Ψ

.

ò

d

l

=

H

t

d

14-3 有一电荷q ，以速度v(v<<c)作匀速

q

d

Φ

a

cos

)

(

1

=

0

d

l

=

H

2

.

d

t

H

q

Φ

d

=

d

S

D

S

=

ò

ò

ò

ò

π

.

r

4

2

s

s

R

q

a

π

ò

2

sin

q

d

q

r

=

q

2

v

π

r

4

2

0

a

ò

q

a

d

Φ

d

I

a

sin

0

=

=

d

d

t

d

t

2

a

d

a

r

v

sin

=

d

t

q

q

a

v

d

a

a

sin

sin

2

ò

=

d

l

=

H

r

2

d

t

2

.

qv

2pRH

a

sin

=

2

r

2

rsina

R

=

qv

sina

H

=

4pr

2

14-4 当导线中有交流电流时，证明：其

γ=5.7×107S/m，分别计算当铜导线载有

dE

δ

g

δ

=

E

=

d

dt

ω

δ

g

sin

t

=

e

e

e

e

e

δ

ω

ω

E0

cos

t

=

E0

d

0

0

0

0

0

ω

sin

t

E

E0

=

δ

g

(

(

(

(

(

(

)

)

)

)

)

)

m

=

ω

δ

d

m

δ

g

5.7×107

m

=

=

=

2.0×1016

2pf

8.85×10-12×2p×50

δ

5.7×107

d

m

=

=

2.0×1016

8.85×10-12×2p×3×1011

δ

g

m

=

2pf

δ

d

m

14-5 有一平板电容器，极板是半径为R

q

d

d

D

S

d

=

d

l

=

d

S

D

H

d

d

t

t

.

.

d

t

r

d

D

d

p

D

H

=

2pr

r2

H

=

d

t

2

d

t

r

q

d

ò

ò

H

=

s

d

2S

t

(

)

r

d

ω

sin

t

=

q0

d

2S

t

r

ò

ω

ω

cos

t

q0

=

p

2

R2

14-6 为了在一个1.0mF的电容器内产生

1.0A的瞬时位移电流，加在电容器上的电压

Id

dU

dU

=

Id

C

=

dt

C

dt

1.0

=

=1.6×106(V)

1.0×10-6

14-7 一圆形极板电容器，极板的面积为

S ，两极板的间距为 d 。一根长为d 的极细

U =U0sinωt，求:

(1)细导线中的电流;

(2)通过电容器的位移电流;

(3)通过极板外接线中的电流;

(4)极板间离轴线为r 处的磁场强度。设r

Id

´

I

=

+

I

S

ω

ω

0

cos

t

+

U

e

e

d

U

0

0

I

=

0

0

U

U

ω

ω

R

sin

sin

t

t

=

=

R

R

dU

Id

C

=

dt

S

ω

ω

0

cos

t

U

=

d

(2)

(3)

´

d

l

=

H

I

.

e

e

0

0

H2pr

Id

I

=

+

pr2

0

U

ω

ω

ω

sin

t

0

cos

t

+

U

=

d

R

ò

1

pr2

0

U

ω

ω

ω

sin

t

0

cos

t

H

+

U

=

2pr

d

R

(4)

B

B

B

x

y

z

.

Δ

B

=

+

+

=0

x

y

z

14-8 已知无限长载流导线在空间任一点

B

B

B

x

y

z

.

Δ

B

=

+

+

=0

x

y

z

m0I

sinq

Bx

=

2pr

m0Iy

m0Iy

=

=

2pr2

2p(x2+y2)

m0Ix

By

=

Bz

=0

2p(x2+y2)

m0Iy(-2x)

m0Ix(-2y)

.

Δ

B

0

0

=

+

=

+

2p(x2+y2)

2p(x2+y2)

14-9 试从方程式

ρ

.

δ

Δ

D

=

δ

Δ

+

=

H

×

t

t

.

ρ

Δ

=

D

ρ

D

.

δ

δ

Δ

Δ

=

+

=

H

×

t

t

(

)

.

.

.

δ

Δ

Δ

Δ

Δ

+

=

D

H

×

t

ρ

.

0

δ

Δ

+

=

t

.

E

B

2

c

2

2

E

B

14-10 利用电磁场量间的变换关系，证

´

Ex

´

Ex

Bx

Bx

=

=

v

´

By

´

g

Ex

=

g

=

Ez+By

(Ey-vBy )

c2

v

´

Bz

´

g

Ez

=

g

=

Ey+Bz

(Ez+vBy )

c2

.

´

´

Bx

´

´

´

´

´

Ex

´

Bx

Ex

E

B

Bx

Ex

+

=

+

(

(

(

(

)

)

)

)

v

v

2

ExBx

EyEz+EyBy

g

EzBz-vByBz

2

=

+

c2

c2

v

2

v

EyBy

EzBz-vByBz

EyEz

+

c2

c2

v

v

2

2

EyBy

EzBz

ExBx

g

1

2

1

+

=

+

c2

c2

.

E

B

=

(1)

=ExBx+EyBy+EzBz

2

2

B

E

=

´

´

c2

B

2

2

E

c2

=

Ex

+

Ey

+

Ez

Bx

By

Bz

2

2

2

2

2

2

´

´

´

c2

´

c2

´

´

c2

=

Ex

Bx

2

2

c

=

By

+

Ey

Bz

2

EyBz

Ez

2

EzBy

2

g

+

+

v2

+

2

2

2

2

v2

+

2v

2v

v

v

2

2

Ey

Bz

EyBz

EyBz

+

Ez

By

+

+

2

+

c2

2

2

2

c4

c2

c4

c2

v

v

Ex

2

2

2

+

Ex

Bx

Ey

2

2

2

c

+

g

2

=

1

1

(

(

(

)

)

)

c2

c2

Bz

)

By

2

2

+

+

g

g

(

2

2

v

c2

2

)

(

v

c2

2

Ex

Ey

Ez

Bx

By

2

Bz

2

2

2

2

2

+

+

c2

c2

c2

g

2

=

(2)

0701 АБВГДЕЁЖЗИ

0711 ЙКЛМНОПРСТ

0721 УФХЦЧШЩЪЫЬ

0731 ЭЮЯ

0601 ΑΒΓΔΕΖΗΘΙΚ

0611 ΛΜΝΞΟΠΡΣΤΥ

0621 ΦΧΨΩ

0631αβγδεζηθ

0641ικλμνξοπρσ

0651 τυφχψω

0211 ⒈⒉⒊⒋

0221 ⒌⒍⒎⒏⒐⒑⒒⒓⒔⒕

0231 ⒖⒗⒘⒙⒚⒛⑴⑵⑶⑷

0241 ⑸⑹⑺⑻⑼⑽⑾⑿⒀⒁

0251 ⒂⒃⒄⒅⒆⒇①②③④

0261 ⑤⑥⑦⑧⑨⑩㈠㈡

0271 ㈢㈣㈤㈥㈦㈧㈨㈩

0281 ⅠⅡⅢⅣⅤⅥⅦⅧⅨⅩ

0291 ⅪⅫⅩ

0101 　、。·ˉˇ¨〃々—

0111 ～‖…‘’“”〔〕〈

0121 〉《》「」『』〖〗【

0131 】±×÷∶∧∨∑∏∪

0141 ∩∈∷√⊥∥∠⌒⊙∫

0151 ∮≡≌≈∽∝≠≮≯≤

0161 ≥∞∵∴♂♀°′″℃

0171 ＄¤￠￡‰§№☆★○

0181 ●◎◇◆□■△▲※→

0191 ←↑↓〓→耻虫仇

0201 ⅰⅱⅲⅳⅴⅵⅶⅷⅸⅹ