tu truong dung 2013 mk

8/12/2019 Tu Truong Dung 2013 Mk

1/62

L thuyt trng in t

Ttrng dng

Nguyn Cng Phng


2/62

Ttrng dng - sites.google.com/site/ncpdhbkhn 2

Ni dungI. Gii thiu

II. Gii tch vct

III. Lut Coulomb & cng in trng

IV. Dch chuyn in, lut Gauss & iveV. Nng lng & in th

VI. Dng in & vt dn

VII. in mi & in dungVIII.Cc phng trnh Poisson & LaplaceIX. Ttrng dngX. Lc t& in cm

XI. Tr ng bin thin & hphng trnh MaxwellXII. Sng phng

XIII.Phn x& tn xsng phngXIV.Dn sng & bc x


3/62


Ttrng dng (1)

1. Lut Biot Savart

2. Lut dng in ton phn tnh

3. Rta

4. nh l Stokes

5. Tthng & cng tcm

6. Tth

7. Chng minh cc lut ca ttrng dng


4/62


Ttrng dng (2)

Ttrng dng (tnh) sinh ra t:

Nam chm vnh cuin trng bin thin tuyn tnh theo thi gian

Dng in mt chiu

Chxt vi phn dng mt chiu trong chn khng


5/62


Lut Biot Savart (1)

2 34 4

RId Idd R R

L a L RH

1 1 122 2

124

I dd

R

L aH

dL1R12

aR12I1

P

2 24 4

L a L aH H R

Id Idd

R R

H: cng ttrng (A/m)

Hng ca H tun theo quy tc vn nt chai


6/62


Lut Biot Savart (2)

K

b

I

I Kb

I KdN

Id dSL K

2 24 4

R R

S

d dS

R R L a K aH


7/62


Lut Biot Savart (3)

12 ' zz R a a

1 122 2

124

Idd

R

L aH

122 2

'

'

zR

z

z

a aa

2 2 2 3/2

' ( ' )

4 ( ' )

z zIdz zd

z

a a aH

1 ' zd dzL a

2 2 2 3/2

' ( ' )

4 ( ' )

z zIdz z

z

a a aH

; 0z z z a a a a a

2 2 2 3/2'

4 ( ' )dzI

z

aH

2 2 3/2'

4 ( ' )I dz

z

a

2

I

a

'

2 2 2

'

'

4 '

z

z

I z

z

a

1

2

x y

zdL

I

R12

aR

zaz

a


8/62


Lut Biot Savart (4)

x y

z

I

1

22 1(sin sin )4

I

H a

x y

zdL

I

R12

aR

zaz

a

2

I

H a

z x

y

z

0

a

a

az

1

2


9/62


Lut Biot Savart (5)

2

I

H a

-1-0.5

0

0.5

1

-1

-0.5

0

0.5

1

-6

-4

-2

0

2

4

6


10/62


Ttrng dng

Lut Biot Savart

Lut dngin ton phn tnh Rta

nh l Stokes

T thng & cng t cm

T th

Chng minh cc lut ca t trng dng


11/62


Lut dng in ton phn tnh (1)

.H Ld II


12/62



2

I

H a

x y

zdL

I

R12

aR

zaz

a

H aH

2

0.H Ld H d

tg( )L a ad d d

.H Ld I

2

0d

2 I

2

H

V d1

dL

I


13/62


II

ab

c

Lut dng in ton phn tnh (3)V d2

1

1

1

1

)(2 b

I

H a

2H

I

:a2

2I I

a

2I H

2

22 H I

a

2( )

2I a

a


14/62


II

ab

c


)(2

bI

H a

0bao k n dy dn trong dy dn ngoiI I I I I :c

2( )

2I a

a

0 ( )c


15/62


II

ab

c


)(2

bI

H a

baokn

2

IH

2( )

2I a

a

0 ( )c

2 2

2 2( )

2

I cb c

c b

:b c 2 2 2 2

2 2 2 2bao k n dy dn trong mt phn dy dn ngoib c

I I I I I Ic b c b


16/62


II

ab

c


2)( ); (

22

bI

H I a H a

a

2 2

2 2( ); 0 ( )

2

I cb c H c

c b

a3a

4a

2I

a

4

I

a

0 2a 4a c3a b


17/62



x

y

z

K=Kyay

L

2

2

1

1

3

3

1 2 ( )x x yL H L K L

1 2x x y

H K

3 1x xH

3 2x x yH K

1( 0)2

1( 0)

2

x y

x y

H K z

H K z

12

N H K a

z

K=Kyay

K= Kyay

h

0(0 )

0 ( 0, )

N z h

z z h

H K a

H


18/62


Ttrng dng

1. Lut Biot Savart

2. Lut dng in ton phn tnh3. Rta (xoy, cun)

4. nh l Stokes

5. Tthng & cng tcm

6. Tth



19/62


Rta (1)

1 2 ,1 2( )H. L yH y

,1 2 0

1

2

yy y

HH H x

x

1 2 0 1( )2

H. L yyH

H x yx

z

x y

x

y1 2

34

H = H0 =Hx0ax +Hy0ay +Hz0az

2 3 ,2 3 0

1( ) ( )

2H. L xx x

HH x H y x

y

3 4 0

1( )

2H. L

yy

HH x y

x

4 1 0

1( )

2H. L x

x

HH y x

y

.H Ld I


20/62


Rta (2)

1 2 01( )2

H. L yy

HH x yx

2 3 0

1( )

2

H. L xxH

H y x

y

3 4 0

1( )

2H. L

yy

HH x y

x

4 1 0

1( ) 2H. L

xx

HH y xy

.H Ld I

.H L y xH H

d x yx y

1 2 2 3

3 4 4 1

. ( ) ( )

( ) ( )

H L H. L H. L

H. L H. L

d

z

x y

x

y1 2

34

H = H0 =Hx0ax +Hy0ay +Hz0az


21/62


22/62


Rta (4)

, 0

.lim

y xz

x y

d H H

x y x y

H L

, 0

.lim

H L yzx

y z

d HH

y z y z

, 0

.lim

H Lx z y

z x

d H H

z x z x

0

.

rot limNN S N

d

S

H LH

t

-SN: mt phng cang tch phn kn- (rotH)N: thnh phn ca rotH vung gc viSN


23/62


Rta (5)

0

.rot lim

N

NS N

d

S

H LH

rot y yx xz z

x y z

H HH HH H

y z z x x y

H a a a

rot

x y z

x y z

x y zH H H

a a a

H

rot H H


24/62


Rta (6)

rot y yx xz zx y zH H

H HH Hy z z x x y

H H a a a

( )1 1 1z z z

H H H HH H

z z

H a a a

( sin ) ( )1 1 1

sin sin

( )1

rr

r

H rHH H

r r r

rH H

r r

H a a

a


25/62

Rta (7)


V d

Tm rta ca cc vctsau:

2 2

2

2

)

sin) cos

cos sin

) sin cos

x y z

z

r

a x y y z xy

zb

c r r

A a a a

B a a

C a a


26/62


27/62


Rta (9)

rot y yx xz z

x y z

H HH HH H

y z z x x y

H H a a a


28/62


Rta (10)

rot H= H a a ay yx xz z

x y z

H HH HH H

y z z x x y

, 0

.lim

y xz

x y

d H H

x y x y

H L

, 0

.lim

H Lyz x

y z

d HH

y z y z

, 0

.lim

H Lx z

yz x

d H H

z x z x

H J

(Phng trnh Maxwell 2)


29/62


Ttrng dng

1. Lut Biot Savart


4. nh l Stokes

5. Tthng & cng tcm

6. Tth



30/62


S

S

S

S

aNnh l Stokes (1)

IJ NN

S

.H L

J

S

N

d

S

.I H LN Sd ( )J HN N

.( ) ( ).

H LH H a

S

N N

d

S

. ( ). ( ).H L H a H SS Nd S

. ( ).H L H SS

d d

S


31/62


nh l Stokes (2)

x

y

z

= 0,25 r = 5

1

2

3

V d1

. ( ).H L H SS

d d

x

y

z

dr

rd

rsind

sinL a a ard dr rd r d

Cho H = 6rsinar+ 18rsincosa A/m.

Kim nghim nh l Stokes.


32/62


nh l Stokes (3)V d1

. ( ).H L H SS

d d sinL a a ard dr rd r d

. .( sin )H L H a a ard dr rd r d

1,2,31, 2,3 : 5 0r dr

sinrH dr H rd H r d xy

z

= 0,25 r = 5

1

2

3

1 2 3r r r r H dr H dr H dr H dr

0rH dr

0H

H rd 0H rd




33/62


nh l Stokes (4)V d1

. ( ).H L H SS

d d . sinH L rd H dr H rd H r d

0rH dr

x

y

z

= 0,25 r = 5

1

2

3

1 2 3sin sin sin sinH r d H r d H r d H r d

0H rd

2sin sinH r d H r d

1,31,3 : const 0d




34/62


nh l Stokes (5)V d1

. ( ).H L H SS


0rH dr

x

y

z

= 0,25 r = 5

1

2

3

2. sinH Ld H r d

0H rd

2sin sinH r d H r d

0,25

0sinH r d

0,25

205sin(0,22 )H d

0,25

203,19H d




35/62


nh l Stokes (6)V d1

. ( ).H L H SS


x

y

z

= 0,25 r = 5

1

2

3

218.5.sin(0, 22 )cosH

0,25

20 3,19H d

57,37cos

0,25

0. 3,19.57,37cosH Ld d

0,25

0 182,84cos d

0,250

182,84sin 182,84sin(0,25 ) 129,27 A




36/62


nh l Stokes (7)V d1

. ( ).H L H SS

d d . 129,27 AH Ld

x

y

z

= 0,25 r = 5

1

2

3

( ).H SS d ( sin )1sin

( ) ( )1 1 1sin

H a

a a

r

r r

H H

r

rH rHH Hr r r r

1 1 1

36 sin cos cos 6 cos 36 sin cossin sin

a arr r rr r




37/62


nh l Stokes (8)V d1

. ( ).H L H SS

d d . 129,27 AH Ld

x

y

z

= 0,25 r = 5

1

2

3

( ).H SS d

1 1 1

36 sin cos cos 6 cos 36 sin cossin sin

a a SrSr r r d

r r

1

36cos cos 6cos 36sin cossin

a a SrSd




38/62


nh l Stokes (9)

x

y

z

= 0,25 r = 5

1

2

3

V d1

( ).H SS

d

x

y

z

dr

rd

rsind

2 sinS ard r d d




39/62


nh l Stokes (10)V d1

. ( ).H L H SS

d d . 129,27 AH Ld

x

y

z

= 0,25 r = 5

1

2

3

( ).H SS

d 1

36cos cos 6cos 36sin cossin

a a SrSd

2 sinS ard r d d

( ). 36cos cosH S a SrS Sd d

2(36cos cos )(5) sinS

d d




40/62


nh l Stokes (11)V d1

. ( ).H L H SS

d d . 129,27 AH Ld

x

y

z

= 0,25 r = 5

1

2

3

2

( ). (36cos cos )(5) sinH SS Sd d d 0,25 0,22 2

0 0(36cos cos )(5) sin d d

0,220,25

20

0

1900 sin cos2

d

0,25

0 182,84cos d

0,25

0182,84cos d

0,25

0182,84sin 129,27 A




41/62


nh l Stokes (12)

( )H . S J. Sd d

H J

.H Ld I

I

V d2

.H Ld IRt cng thc t H J

( )H . S J. SS S

d d . ( ).H L H S

Sd d


42/62


Ttrng dng

1. Lut Biot Savart


4. nh l Stokes

5. Tthng & cng tcm

6. Tth



43/62


Tthng & cng tcm (1)

nh ngha cng tcm B trong mi trng tdo:

B = 0H n v: Wb/m2 hoc T hoc G (1T = 10000G)

0 = 4.107 H/m

nh ngha tthng (dng t):

Nhc li vthng lng:

.B SS

d

.D SS d Q


44/62


Tthng & cng tcm (2)

Lut Gauss cho ttrng:

Theo nh l ive rt ra c p/trnh Maxwell 4:

Bcc phng trnh Maxwell:

. 0S d B S

0.B

0

0

.D

EH J

.B

v

0

. 0

D. S

E. L

H. L J. S

B S

vS V

S

S

d Q dv

d

d I d

d


45/62


46/62


Ttrng dng

1. Lut Biot Savart


4. nh l Stokes

5. Tthng & cng tcm

6. Tth



47/62


Tth(1)

nh ngha tthVm theo cng thc:

V nn:

V rta ca gradient ca mt i lng v hng phibng zero nn:

H mV H J

( )H J mV

( 0)mV H J

0.B 0 0.B .H

0 ( ) 0. mV 2 0 ( 0)JmV


48/62


a b c

Irax

y

Tth(2)P(, /4, 0)

: 0Jba

)(2 b

I

a H a

( 0)H JmV

12

mm

VI V

2

mV

2mV

1 ( 0, 1, 2, ...)8

I n n

12 ( 0, 1, 2, ...)

2 4mP

IV n n

0t 0mV


49/62


Tth(3)

nh ngha vcttthA theo cng thc:

n v: Wb/m

V nn

C thtnh A theo cng thc:

B A

0 0

1 1

H B A 0

1

H J A

0

4

LA

Id

R

dL R

aRI

P

0

4

LA

Idd

R


50/62


Tth(4)

0

2 24A az

Idz

d z

x

y

z

z

IdL =Idzaz

2 2

R z P(, ,z)

0

4

LA

Idd

R

2 2R z

L azd dz

0

2 2 0 04

a

A A A

z

z

Idz

d d dz

0

1H A

0

1H Ad d

0

1az

dA

2 2 3/ 24 ( )H a

Idzd

z


51/62


Tth(5)

Nu c mt dng in J chy trong mt khi no th:

IdL = Jdv

0

4

LA

Idd

R

04

JA V

dv

R


52/62


Ttrng dng

1. Lut Biot Savart


4. nh l Stokes

5. Tthng & cng tcm

6. Tth



53/62


(1)

Dng cc cng thc/nh ngha

chng minh cng thc

0

4

JA

V

dv

R

024

L aH B H B ARId

R

024 4

J L aA H

V

dv Id

R R


54/62


(2)0

24 4

J L aA H

V

dv Id

R R

0 1 12124

JAV

dvR

Gisvi phn dng (x1,y1,z1), A

(x2,y2,z2)

0 1 12 2 22

0 0 124

JAH

V

dv

R

0

0 0

B H B AH

B A

1 12

12

1

4

J

V

dv

R 12 1

12

1

4

J

Vdv

R

( ) ( ) ( )V V VS S S

2 2 1 2 1 112 12

1 1 1

4J J

VH dv

R R


55/62


(3)0

24 4

J L aA H

V

dv Id

R R

Gisvi phn dng (x1,y1,z1), A(x2,y2,z2)

2 2 1 2 1 112 12

1 1 1

4J J

VH dv

R R

2 1 0J

2 2 1 112

1 1

4J

VH dv

R

2 2 212 2 1 2 1 2 1( ) ( ) ( )R x x y y z z 12 122 3 212 12 12

1 R a

R R R

12 12 12

12

1

4

a JH R

Vdv

R

1 12 12

12

1

4

J aRV

dvR


56/62


(4)0

24 4

J L aA H

V

dv Id

R R

Gisvi phn dng (x1,y1,z1), A(x2,y2,z2)

1 1 122 2124

L aH RI dR

1 122 12

12

1

4

J aH R

Vdv

R

1 1 1 1J Ldv I d


57/62


(5)

H J

0B H H J

B A

2 2 2 2x x y y z zA A A A a a a

2

( ) A .A A

0 0

1

BH A

2

0

( )

.A AH


58/62


(6)

H J

0 1 1

2124

V

dv

R

J

A

2

0

( )

.A AH

.( ) ( ) ( )S S S A A. .A

02 2 1 2 2 1 1

12 12

1 1( )

4 Vdv

R R

.A J . .J


59/62


(7)

H J

02 2 1 1 1

12

1

4 Vdv

R

.A J .

121 23

12 1212

1 1

R RR

R

2 1 112

1

( ) 0V dvR

.J

02 2 1 2 2 1 112 12

1 1 ( )4 V

dvR R

.A J . .J


60/62


(8)

H J

02 2 1 1 112

14 V

dvR

.A J .

.( ) ( ) ( )S S S A A. .A

0 12 2 1 1 1 112 12

1( )

4 Vdv

R R

J

.A .J .


61/62


(9)

H J

1

0 12 2 1

12

04 S

dR

J.A S

1 1 0

v

t

.J

S Vd dv J. S .J

0 12 2 1 1 1 112 12

1( )

4 Vdv

R R

J.A .J .


62/62


(10) H J

0 .A

04

v

V

dvV

R

0

4

xx

V

dvA

R

2

0

( )

.A AH

2

0

2

0

2

0

x x

y y

z z

JJ

J

2

0

vV

H J

2

0 A J

tu truong dung 2013 mk

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