Electromagnetics in Arabic

8/2/2019 Electromagnetics in Arabic

1/88

:- .

- .

-.

- .

. -.

-.

( ) . . . .

()

. ()

. ( ( .

1-1-: . ( ) .

1


2/88

(). .

1-1-1-:

1.67 10-27 kg

(+) . 9.11 10-31 kg

C (-) 1.67 10-19 C.

) :- () (

( ( )) :-Point Charge -.C q

) :-Line Charge( - q C L

L / C/m.) :-Surface Charge( - q C

S .C/m2 / s

q C ) :-Volume Charge( - V v

.C/m3 / )1-1( .

( ) ( ).

2

z

y

x

L C/m

s

C/m2

v

C/m3

q1

C

q2

C

q3

CS

L

V


3/88

) :-1-1( :- q1 Cq2Cq3 C L C/m s C/m2

v C/m2.:-2-1-1

)Coloumb Law( )Electric Force) F) (

q1 Cq2 C R12 )2-1(:-

NR4

qq12R2

12

2112 aF

= (1 - 1)

F12 q1 q2 F12 = -F21 121212R rrR == q1q2

12Ra 1r2r

) (m/F)36/(109

0 =

. )2-1(r1r2R12aR12 :-

z2,1y2,1x2,12,1r2,1z2,12,1r2,12,1zyxrzr aaaaaar ++==+=

z2,1y2,12,1x2,12,1zsinrcosr aaa ++=

z2,12,1y2,12,12,1x2,12,12,1cosrsinsinrcossinr aaa ++=

212

212

2121212 )zz()yy()xx(R ++== rr

12z12y12x1212RR/])zz()yy()xx[( aaaa ++=

3

q1

(x1y,

1z,

1)

(r1,

1,

1

) q 2(x

2y,

2z,

2)

(r2

,2

,2 )1r

12R

2r

12F

21F

z

y

x

) :-2-1(F

21 q

1

q2

R 21

.

(r2,

,2z

2)

(r1,

,1z

1)


4/88

)1-1( .

q1 ( )

2212 mR4

q2.

E (Electric Field( E1 )x2, y2, z2(

q1 )x1, y1, z1(:-

m/VR4

q

q 12R12

1

2

121 a

FE

== (2 - 1)

N/CV/m. 'V V )3-1(

)x, y, z(:-

m/VR4

dV)r(R

'V

2

''V aE(r)

= (3 - 1)

'R r-r=RRa /R =.

4

'r

Rz

y

x

r

dV'

V

V'

)r(E

) :-3-1(

.


5/88

))4-1 ) :-1-1(q1 = 1 nC )1,0,0(q2 = - 2 nC )0,0,0(q3

= 1 nC -)1,0,0(:-)i( ) )ii . ))iii .

P1 (x, y, z( P2 P3)0,0,1) (2,0,0.(

:-)i(

29x

99

121)36/10(4

)()102()101(

= aF nN18 xa=

29x

99

132)36/10(4

)()101()101(

=

aF nN25.2 xa=

)ii( :-

xx13123121 25.218 aaFFFFF +==+= nN75.15 xa=

)iii( P1

5

x

y

z

-)1,0,0(

)1,0,0(

P3

0 ,0 ,2))

P2

1 ,0 ,0))P1

)z ,y ,x)

q3

1 = nC

q2

2- = nCq1

1 = nC

) :-4-1( )1-1.(


6/88

[ ]

++

++

=

2/3222

zyx9

9

zy)1x(

zy)1x(

)36/10(4

10)z,y,x(

aaaE

[ ] [ ]m/V

zy)1x(zy)1x(

zyx(zyx(2

2/3222)zyx

2/3222

)zyx

+++++++

++++ aaaaaa

P2:-

[ ]22/)(2)22(/)(9)1,0,0( zxzzx aaaaaE +++= m/V64.11 za=

P3:-

[ )11.05.0(9)0,0,2( xxx aaaE += m/V5.5 xa=

))5-1 ) :-2-1( LC/m z

.)P (0, y, 0

:-

Cdz 'dz 'L dE:-

6

x

y

z

(0,0, -z')

(0,0,z')

zd'

Ed

P(0,0 ,y)

) :-5-1(

z.

R

Ed


7/88

m/VR4

dz)0,y,0(d R2

0

'L aE

=

2/12'2

)zy(R =+2/12'2

z'

yr )zy/()zy( += aaa.

:-

m/Vdz

)zy(

)zy(

4)0,y,0( '

2/32'2

z'

y

0

L

+

=

aaE

ay )E (

= Ey ay

2/32'2

'

0

Ly

)zy(

dz

4

y2)0,y,0(E

+

=

= tanyz '

= 2' cos/yddz=+ 232/32'2 cos/y)zy(

2

2/

0

2

02/32'2

'

y/1dcosy

1

)zy(

dz==

+

)0,y,0(:- m/V)y2/()0,y,0(E 0Ly =

ar:-

m/Vr2

)z,,r(E0

Lr

=

r .

:-3-1-1 V (Electric Potential(

7


8/88

. +q ))6-1

P1(r1( )P2(r2 )P1(r1

. )(P )P1(r1 '2

'2 r

. -:

=2

1

12V dLE V (4 - 1)

E. ) (

EddL . dLzyx dzdydx aaadL =++

zr dzrddr aaadL ++= ++= aaadL dsinrrddr r.

) :-6-1( +q .

)6-1(dL = drar m/Vr4q

r20

aE

=

V12:-

8

+q)(P 22 r

)(P'

2'

2 r2r

1r

r

E

P1)r

1)


9/88

Vr

1

r

1

4

qdr

r4

qV

120

2r

1r2

012

=

=

r2 = rr1 ) P r(

Vr4

q)r(V

0= (5 - 1)

r V)r4/(q 0

)7-1(

))5-1 .

'dV:-

R

dV

4

1)r(V

'v

'V0

= (6 - 1) R 'v dV

. ) )

.

9

qV

1 V2 V

3 V4

E

) :-7-1( E

.


10/88

V12 ) )2-1:-)3-1(

r2 r2 r1 < r1. 2L z z = - Lz = L

.m/CL )0,y, 0(

:- )r2/(E 0Lr =

(r = r1 V12 (r = r2:-

++== )dzrddr(r2V zrr0L12 aaaadLE

Vr

rln

2r

dr

2 2

1

0

L2r

1r0

L

=

=

LzL

V )0,y, 0(:-

R

dz

4

1)0,y,0(V

'L

L

L0

=

2'2

'L

L0

L

zy

dz

4+

=

))tanyz ' =

= 2' cos/dydz

=+

cos

yzy

V 2'2

:-

+

=

=

1

1

0

L1

10

L

sin1

sin1ln

4cos

d

4)0,y,0(V

= y

Ltan 11

10


11/88

VLyL

LyLln

4)0,y,0(V

22

22

0

L

+

++

=

)8-1(

V1V2 V1 - V2V2 - V1. .

EdL E dL dL

.E dL dL

.

) :-8-1(.

:-4-1-1 )Voltage Gradient(+ VV V L

E )9-1(

:-

=2

dLE

1

L12 LEVV

EL L

L/VEL (7 - 1)

11

E

V2

V1

V12

V21

V12

E

E


12/88

. dL = dx axx

VEx

)x

VE(

xxxaaE

=

dL= dy ayy

VEy

dL = dz azz

VE z

dL = dx ax + dy ay + dz az

E :-

+

+

++= zyxzzyyxx zV

x

V

x

VEEE aaaaaaE

) :-9-1( VV + V L E.

0 dLL:-

+

+

= zyx zV

y

V

y

VaaaE

)z,y,x(Vzyx zyx ++=aaa (8a - 1)

V=E (8b - 1)

zyx zyxaaa

+

+

)gradient(

:- .

12

x

y

x)2y,

2(

L

Ld

E V

+V V

E

Ld


13/88

:-

+

+

aaa

sinrrr r

,V(r ) :-4-1(:- , ) = 50 /r V (i(

. . V(x,y,z) = 5 x2 y V (ii)

:-

)i( )8a - 1( m/V

r

50V r2 aE ==

)ii( )8a - 1(

m/Vx5yx10V y2

x aaE ==

:-5-1-1 D

))3-1 :-

m/Vr4

q1r2

aE

=

. r

22 m/C)r4/q( )electric flux density) D displacement vector

2r2

m/Cr4

q aD

= (9a - 1)

ED = (9b - 1)

)9a-1( . D:- 'V v

13

zr zrraaa

+

+


14/88

2

'V

r2

'v m/C

R4

dV

= aD (10 - 1)

q ))9a-1

D )10-1.( ( .( q q

:-

=

=0

2

0

r2

r2S

qddsinrr4

qaadSD

:- dVq v

VS

== dSD (11 - 1)

) q ) ))11-1

( ( S D . V . ( )

S(Closed )Gauss Law( )11-1(Surface( )Gauss Surface.(

D

.

14

Dq

V

S

) :-01-1( q S

.D


15/88

))11-1 ) :-5-1(m/CL D E

.

:-

L )11-

1.( D ra z

2rr m/C)r(D aD =

) :-11-1( m/CL.

:-

( ) =

++=

L

L

3S2S1SS

dzdSDdSD

S3 S2 S1

:-

2LrLrL

2 L

0

r m/Cr2DLDLr2LdzrdD

===

=

m/V)r2/(/DE 0L0rr ==

15

x

y

z

r D

S

3

S 1

S 2


16/88

2-1.

E D :-)6-1( 2s m/C

xyz = 0 )12-1.(

:- D x y

z zzD aD = L )12-1(

:-

=

++=

+++ S

s

6S5S4S3S2S1SS

dS)( dSDdSD

) :-12-1( 2

s m/C.

S3S4S5S6 :-

2sz

2s

2z

2z m/C2/DLLDLD ==+

m/V2/E sz =

16

z

y

x

L

D

D

S

1

S

2

m/C 2

s

,5S ,4S ,3S6S


17/88

a ))13-1 ) :-7-1(3v m/C .

.

:- D

r 2rr m/C)r(D aD = D ar0

=

=

=

ddsinrD 22

0 0

r

1S

dSD

=2

0 0

r

0

'2'v dddrsinr

2vrv3

r2 m/C

3

rDr

3

4Dr4

=

=

m/V3

rE vr

=

r > a

=2

0 0

2r

2S

ddsinrDdSD =

ddsinr22

0 0

a

0

v

17

y

x

z

a

S1

S2

v

rr`

v

) :-31-1(

a .


18/88

22v

3

rv3

r2 m/C

r3

aDa

3

4Dr4

=

=

)r > a(

m/Vr3aE 2v

3

r=


19/88

zyx zyxaaa

+

+

)12-1(

D (Divergence ofD( . )6-III(D.

)) :-8-12

zyx m/Cnzyx aaaD ++=

2m.

:- )12-1(:-

zD

yD

xD zyx

v +

+

== D 2m/Cn3111 =++=

:-

nC24dzdydx3Q

2

o

2

o

2

o

== D) )7-1) :-9-1( > a < r .

:- )7-1( a < r< D:-

22v

3

r m/Cr3

aD

=

)6-III( D ) )D rr aD =:-

00)Dr(rr

1r

22v

++

== D 3m/C0=

>> ra.

:-7-1-1 )Poisson's & Laplace's equations( )(V r )(v r

)(rD)(V rv= D== /V DE

=

D)V(

19


20/88

r)(r DD

=

1

=v2

)(V r (13 - 1)

22

2

2

2

22

zyx

+

+

)Laplacian( )6-III(. )13-1(

.:-

0V2 = (14 - 1)

.

)14-1( :-)10-1(a b

V0 0V

V (r, ,z(.

:-

. zV (r, ,z( z r

:-

00

r

V

r

1

r

V0)z,,r(V

2

22 ++

+

==

0rd

Vdr

rd

d

r

1

rd

Vd

r

1

rd

Vd2

2

=

=+

20

b

ra

br

a

0 V

0 V

0

V0

Vo

z


21/88

:-)14-1( V0 V.

:- B)r(LnA)r(V +=

0V)a(V 0)b(V= =B)a(LnAV0 =+B)b(LnA0 +=

)a/b(Ln)b(LnVB 0= )a/b(Ln/VA 0=

V)a/b(Ln

)r/b(LnV)r(V 0=

:-8-1-1 )electric dipole(

. L

r r >> L )15-1( .

)r, , 0(:-

Vr

1

r

1

4

q

),r(V

= +

( ) ( ) ( )( ) 21

222 cosr/Lr2/L1rcosrL2/Lrr +=+= .

21

q

q

y

r

r+

r-

(r,,0)

x

z

L/2

L/2 ) :-51-1( +qq-

L.


22/88

r >> L r )Taylor Series(:-

[ ] += cos)2/L(r...cos)r2/L(1rr

( )

222

cos2/Lr

cosL

4

q),r(V

Vcosr4

qL),r(V

2

= (15 - 1)

E V=E E:-

rr EE aaE += (16 - 1)

= cosr2

qLE 3r= sin

r4qLE 3.

+ qL az:-

CmqLq ze aLm == (17 - 1) )Electric Dipole Moment(

)15-1()16-1(:-

Vr4

),r(V 2re = am (18 a - 1)

( ) m/Vsincos2r4

r3e

+

= aam

E (18 b - 1)

)16-1( me.

22

q

q

V=0 Lm qe =


23/88

:-)16-1( Cmqe Lm =.

))Dielectric Materials 9-1-1-: ( (

( ( . ) ( ) )

Cmqe Lm =L )

( .N 3mV :-

2e m/CV

NP

m

(19 - 1)

P )polarization vector( D

V )N(

)17-1(

VV0 d )vacuum( )17a - 1(

:-

23


24/88

m/Vd

Vx

0 aE = (20 a - 1)

)fringing(

m/Vd

V 0x0

00 EaD == (20 b - 1)

)17b-1(.

)bounded charges( ) 1-1

. ) . ( )

. ( ) .

P PDD += 0

PED += 0 (21 a - 1)

d

V0== ED (21 b - 1)

:-

E

P

E

D+== 0 (22 - 1)

:-)17-1( V0 (a( )b(.

-: )22-1(

24

d

1 1

E

(a) (b)

V0

(V) V0 (V)

E 0


25/88

+==

D

P100r (23 - 1)

r )1-1(r.

r):-)1-1

r 1

1.0006 ) )

2.1 3

4 6 81

P :-

DEEP )1()1()( r0r0 === (24 - 1) D P

) ( .

))Boundary Conditions 10-1-1-: )18-1(

E1D1 E2D2

: E1tE2tDt1 D2nD1nE2nE1n D2t .

-Dn:- ) (h 2,1S

)18-1( . :-

25


26/88

dSDdSD

++=

3S2S1SS

dhdV vhS

v

V

==

dS (25 - 1)

h ( (3S

dhvh

2

svh

0hm/CdhLim

= -: )25-1( SDSDSD s22n11n

1S2S ) S ( :-

2s2n1n m/CDD = (26 a - 1)

Dn

2n1n DD = (26 b - 1)

26

L

h

1 h

11 D,E

11 ttD,E

11 nnD,E

2tE

1tE

2nD

1nD

na

ta

22 D,E E,D 22 nn

22tt D,E

S

S3

S1 S

2

2

1


27/88

:-)18-1( ED 12.

:-

2s2n21n1 m/CEE = (27 a - 1)

2n21n1 EE = (27 b - 1)

.

- Et:- )18-1(

1-4-3-2-1 =1

2

2

1

dLEdLE

dLE

0

1

4

4

3

3

2

2

1

=

+++= dLEdLE

Et h

3

2

1

4

:-0LELE 1t2t

L :-

2t1t EE = (28 - 1)

) .(

:-

2

2t

1

1t DD

=

(29 - 1)

27


28/88

Dn

En

0

D0E ==

s=1/ n C/m2

)27b - 1()28-1( 21 .

)26a - 1(s .

. sb :-

sb2n1n PPP = (30 a - 1)

1nP2nP ( )0P 2n =:-

sb1n PP = (30 b - 1)

m/F0))18-1 ) :-11-1(

2m/nC1

.

):-19-1(.

:-

0=D0=E )( . 1t2t E0E 1t2t== D0D ==

s2n1n DD = 0D 2n =

21n m/nC1

D

m/V36=D

E0

1n1n =

))19-1 .=

.

28


29/88

10-1-1-:

)Capacitor( )

Stray Capacitors(.- +q

q V C :-

=dLE

V

v dV

V

qC (30 - 1)

F (Farad(

))parallel plate )20-1( ) :-12-1(0 d m A m2

VVV0 m/F0r . .

. . . ()

:- :-

m/Vd/VE 0z =

2

0r0z m/Cd/VD =

:-EP 0r )1( =

29

d

0V

V0

V))

y

z

E

m A 2

) :-02-1( P


30/88

20rz m/Cd/V)1(P = :-

20r0s m/Cd/V =

2 0r0s m/Cd/V =

. :-2

00rsb m/Cd/V)1( =

2

00rsb m/Cd/V)1( =

. C :-

Fd

A

dV

AV

V

A

V

qC 0r

0

0r0

0

s

0

=

=

==

A d

.

)21-1( ) :-13-1(

a b


31/88

aL)(Lr)DD( 2S1S2r1r +=+

2

2S1S2r1r m/C)(raDD +=+

1r11r ED =2r22r ED = )E(EE r2r1r ==) 120==

( :-

)(r

a)(E 2S1S21r +=+

)(

)(r

aE 2S1S

21

r +

+

=

) :-21-1( )a( )b( .

:-

)a/b(Ln)(

)(aV

21

2S1S

b

a

0 ++

== dLE

)(

)a/b(Ln)(

)(

)a/b(Ln)(aV

212L1L

212S1S0 +

+=+

+=

31

a

r

b

s2

s1

1

2

E2r

, D2r

E1r

, D1r

a

b 2

1

(a)(b)


32/88

m/F)a/b(Ln

)(

V

)(C 21

0

2L1L +=+

=

m/F)a/b(Ln . 1


33/88

r = b:-2

1S m/C55.0 =2

2S m/C11.0 =

m/pF8.51C =

-: - ) (

V . :-

Vqd

dWV e= (32 - 1)

edW dq

qd

Wd

C

qV e== qdq

C

1Wd e =

:-

JqV2

1CV

2

1

C2

qW 2

2

e === (33 a - 1)

JdV

2

1W

V

e DE = (33 b - 1) )33-1(

. m/F S

d 3mSdV = :-

32e

e m/JE21w

VW == (34 a - 1)

3e m/J2

1w DE = (34 b - 1)

a ))22-1 :-)14-1( q C:-)i(

33


34/88

r0

:-2

2r2

r m/Cr4

qDqr4D

==

m/Vr4

qE

20

r

r < aDE=

.

)ii( :-

=r

V dLE

> ra :-

Vr4

qdr

r4

qV

0

r

'

2'0

=

=

> r0 :-

34

ar qC

Er

Dr

0

:-)22-1(

C q .


35/88

Va4

qV

0

r

a

a

=

+=

dLE

.

)iii( :-Fa4V/qC 0==

:-

Ja8

q

)a4(

qa4

2

1CV

2

1qV

2

1W

0

2

20

2

02

=

==

=

:-2-1

I)i(C/s A .

:-

Atd

qdi = (35 - 1)

. .

.

. .( )

.

) ) . .

.

35


36/88

) ) .

.

.

.

.x1x2 x

) ( E x2 x1

t tx

(

. ( )Drift Velocity)

vd

Ev =d

(37 - 1)

)Mobility( )sV/m( 2 .

3v m/C s/mvd 2mA

Avi dv= (38 a - 1)

:-dv vA/iJ == (38 b - 1)

J)J( A vd )Ohm's Law( )V =

IR( V = ELI = JAR = L/( A( L ) (

36


37/88

2m/AEJ = (39 - 1) )Conductivity(.

)1)m ))39-1

2m/AJ( ) E

) .(1)m ) )Resistivity(m1 = .

. ( )

. )2-1( . C20

)1)m ) :-2-1( .

1)m(

10-17

10-15

10-12 10-4 10-3 0.2

2 4

103

3 104

106 5 106

3.5 107 4.1 107 5.7 107

37


38/88

G R (Conductance( :-

==L

)A(/dLdRR (39 a - 1)

==A

1)(L/dAdGG (39 b - 1)

)23-1( ) :-15-1(ba L

.

:--: dR

=ddrr

dzdR

122b

a

)(L

)ab(drr

L

2G

=

=

=)ab(

LR 22

) :-23-1( )a( )b( )c(.

-: dR

38

a

br

z

L I

V0

a

br

z

I

V0

a

br

z

I

V0

(c) (b) (a)


39/88

=

=

= L2)a/b(Ln

Rr

rd

L2

1R

dzrd

drdR

b

a

-: dR

)a/b(Ln2

L

r

dr

2

LG

dzdr

drdR

b

a

=

=

=

=

)a/b(LnL

2R

)37-1()38b-1()39-1(

EvEJ === vdv1

v )m(= (40 a - 1)

sV/m/ 2v= (40 b -1)

.))40a-1 ))40b-1

)DC .

. . )

( .))38a - 1

S)0I( = :-

0S

S

=

dJ (41 a - 1)

0= J (41 b - 1)

3-1-:

.

39


40/88

( )

.

1-3-1-:

( ) .

. .

:-

- )Line Current( :- .A I - )Line Current(:- I A

( )L .=Km/AL/IK

- )Surface Current(:- I A ) (S

2m/A)S/I(J =.

)24-1(.

) :-24-1( I AKA/m J A/m2.

40

L

x

z

y

I

I

I

S m2

J

K


41/88

:-2-3-1 - 2' mS

2m/AJ

)25-1( -Biot-SavartLaw B Magnetic Flux density . 'dV 'dS'dL )z,y,x( )),,r''' '''

) P (x, y, z )),,r dB .

dBJ :-

22

R''

m/Wb

R4

dV)(

=

arJdB (42 - 1)

H/m|||| '

'

Rrr

rr

R

Ra

= R.

)42-1( dBJ .

J aR dB.-: P B

41

x

z (z,y,x)

(,r ,)P

r

R

'r

(z,'y,'x')

(,'r ,'')

J

S'

I

Vd'?B

y

I

) :-52-1( A IB

.P


42/88

='V

'2

R'

dVR

)(

4

arJB(r) (43 - 1)

)26-1( ) :16-1(- z I A .B

))0,,r .

:- B z

)43-1( r

:-

='L

2R

R

I

4

adLB(r)

'

z'dz adL' z=

'z zr aaR =

2'2 zr +=|R|RR/a =R.

+

=+

=0

2/32'2

'

2/32'2

'

)zr(dz

2rI

)zr(dz

4rI)r(B

= tanrz '

=+

3

32/32'2

cos

r)zr(

=

2'

cos

drdz z = 00=

=z2

=

42

(,r0,)

R

r

x

y

z

zadL'' dz=(0,0,z')

za'z

I

) :-62-1( A I.


43/88

22/

02

m/Wbr2

Idcos

r2

rI)r(B

=

=

I )27-1( ) :-17-1(A .a x y

.))0,0,z

:-

z )B )43-1( .(

:-

='L

2R

'

R

I

4)z,0,0(

adLB

'da = adLrz az aaR 22= az +=RRR/a =R.

) :-27-1( I A x y.

:-

43

z

R

'raa

x

y

''

da

'

= adL

(0,0,z)

zz a

I

a

`

'd


44/88

=

+

+

=

+

=2

0

'2/322

zr2

0'2/322

rz''

d)az(

)az(

4

aI

)az(

)az(d

4

aI)z,0,0(

aaaaaB

Br) ar ' B ) Br

:-

22/322

2

z m/Wb)az(2

aI)z,0,0(B

+

=

B 2

z m/Wba2

I

)0,0,0(B

=

3-3-1-:

. ( )I1 A

) I2 A( dL

:-

NI 211 BdLFd = (44 - 1)

dL1 B2

. :-

=2L 1L

2R2121

R)(

4II adLdLF (45 - 1)

- B2 R dL1dL2.

)28-1(

44


45/88

L2L1 L2L1 :-

2

R21

2L2L

21

R

)(

4

II adLdLF

= (46 - 1)

) :-28-1( I1 I2.

L1 ))29-1 ) :-18-1( L2 I A 2m/WbB .

:-)i( 2z1 m/WbB aB =.)ii( . xy

.

) :-29-1( L1 L2 I A .B

45

x

y

z

I

L1

ab

cd

L2

1B

2B

I2

I1

L1

L2

2B RLd

2

Ld1


46/88

:-)i( z1B aB1 = :-

NBLI x12ab1 aF NBLI= y11bc1 aF =NBLI x12cd1 aF NBLI= y11da1 aF =

.

)ii( y2B aB = :-N0ab2 =FNBLI z21bc2 aF =N0cd2 =FNBLI z21da2 aF +=

bcda x

NmBLIL x221 aT zam = 21LIL=

NmBmT = .

3-4-1-: )42-1(

'dL :-

22

R m/WbR

I adLdB

' =

2

R

R

I adL'

)A / m( )Magnetic Field Intensity(

dH H B :-

HB = (47 a - 1)

H :-

='V

'2

R'

dVR

)(

4

1 arJH (47 b - 1)

,)r , 0( I A z :-)161(

r2

IH

=

46


47/88

H= adL dr

Id

2

Idr

r2

I2

0L

=

=

=

=

dLH

:-

dSJdLH == SL

I (48 - 1)

)J(I )Amper's Law( H .

L.

))30-1 ) :-19-1( aIA z .H

> B r0.

:- H z

( ) a )48-1( ar0 i :-

m/Aa2

rIHr

a

Ir2H

2i2

i2i =

=

B :-

47

y

z

x

I

rir

0

) :-03-1(a

A I

.


48/88

22i m/Wb)a2/(rIB =

r0r > a :-

Ir2H 0 = m/A)r2/(IH 0= B :-

20 m/Wb)r2/(IB =

xy )31-1( )20-1(:- xy .

m/AKx0

aK= H .

)31-1(:- yx z=0 m/AK x0 aK=.

:- H x y

)31-1( yL m :-

LK0

1

4

4

3

3

2

2

1L

=

+++= dLHdLH

az |H1| = |H2|

48

x

y

z

K0 A/m

+

-

2 H

1 H

K0

L


49/88

LKdHdH 0

2/L

2/L

yyy2y

2/L

2/L

yyy1y =+

aaaa

m/A2/KHH 02y1y ==

202y1y m/Wb2/KBB ==

5-3-1:- )The Curl & Stocks Theory( JH )48-1(

L S L .LL S

))48-1 S

:-SJdLH

L

H

dLH

J

=

S

Lim L

0S0L

(49 - 1)

J ))49-1 . )32-1(

AI)m/A( 2J ))49-1

. .

49

S

L

LJ

J

L

) :-23-1(

J L

.


50/88

-: )49-1(

dSHdSJdLH ==

SSL (50 - 1) () H.

.

H B .

0mS

== dSB (51 a - 1)

0= B (51 b - 1)

m ) ( . .

.

:-6-3-1 )Magnetic Vector Potential(

- .

A

B :-

='V

'dVR4

)(rJ(r)A

'

(52 a - 1)

(r)A(r)B = (52 b - 1)

50


51/88

A J )52a - 1( )43-1(.

()52a - 1( ))43-1 ))52-152b - 1(

R

Vd

4V

=

)r(JB

r'r)xyz 'x'y'z(

=

'V

'dVR4

)(rJB

'

(53 - 1)

III)21h-III( )R/( )(rJ ' :-

( ) J)(rJ)(rJ ''

+=

R

1

R

1

R

( 0= )(rJ 'r r '( ) 2R R/R/1 a= )53-1( :-

=='V

'2

R dVR4

)(rJa

AB '

==

'V

'

2

R

dVR4

a)(rJ

AB

'

(54 - 1)

.))43-1

))33-1 ) :-21-1( L I A)

(

51


52/88

z .( )A),,r(P r>> L.

:-

A )52a-1( 'dV)(rJ 'z

'dzII adL' =

R

dz

4

IA

'2/L

2/L

z

=

+= cosrz2zrR '2'2 r >> L RR ~ r

Az

m/Wbr4

LIAz

=

= aaA sinAcosA zrz

)sincos(r4LI

r

= aaA

III )19c-III(AB =2

2m/Wbsin

r4

LIAr

r

1

=

= aaB

) ))34-1 :-)22-1(I A S m2)

xy .A

52

y

z

x

R

r

P ( r,,)

2/L

2/L

zaz

'

'dL

I

) :-33-1(

A I.


53/88

B ),,r(P r >> D D .( )

:- A )52a - 1(

'dLJ IdV ' =

R

I

4 'L

'dLA

=

. III-: )22e-III(

=S

'n dSR

1

4

IaA

na)za(

z'y'x'' zyxaaa

=++)z,y,x( '''

2R

3'

RRR

1 aR==

. r >> DR ~ r

aR~ ar A :-

=

= aaaA sinr4

SI

r4

SI2rz2

53

y

z

x

R

r

P (r,,)

'dL

S m 2

D

I

) :-43-1(

yx I

) (.


54/88

IS ) (2

m AmISm zm (= SI am A )=:-

rm2r4 amA

=

B AB =

= aaB )rA(rr

1)sinA(

sinr

1r

[ ] 2r3 m/Wbsincos2

r4

SI+

= aaB

N N .

JH HBA= == :-

H)BA) == ((

)

( JAA) += 2( (55 - 1)

A 0= J0= A JA =2 (56 - 1)

AJ.

)Magnetic Materials( 7-3-1-: () .

)Spinning( .

m2 S I A

2m AmI Sm =) ( .

54


55/88

.

)N( )S( -qmqm)

L Wb ) qmL .

)21-1( Im) ( L

ImL

LqLISI mm (56 -1)

)35-1( ) ( Im .

.

.

.

m/H104 70=

H B :-2

0 m/WbHB = (57 - 1)

V N

2e AmN m m/AV/N e m

H )MagnetizationVector(

)Magnetic Polarization) M

m/AV/N e = mM (58 - 1)

55


56/88

m/AMH + B

:-

HMHB += )(0 (59 a - 1) :-

m/H)/1(00r HM+== (59 b - 1)

) :-35-1( )a( I A )b(

S (c( )d( )e(.

56

(b)(a)

=S

I

Im

(e)

B

1

2

-qm

+qm

(d)

B

N

S

(c)

B

B


57/88

r

. )36-1(

( .(

.

) )

.( )

00

S

== dSBB (60 - 1)

)Ferromagnetic and Ferite( 1r >> 16

)m(10

16

)m(10

.

))boundary conditions 8-3-1-: )37-1(

H1B1

57

N S

N S

N S

N S

N S

N S

N S

N S

N S

N S

N S

N S

(a)

(b)

(c)

H

H

HH

HH

) :-63-1(

)a(

)b()c(.


58/88

H2B2 .

. Bn1Bn2

0

S

=

dSB

Ht1Ht2 . )37-1(.

2,1S -: -Bn

h

( ) 0

3S2S1SS

=

++=

dSBdSB

0h0S3 0S 2,1

2n1n BB = (61 a - 1)

)28-1(

2n21n1 HH = (61 b - 1)

:-)37-1( HB 12.

- Ht:- 4-3-2-1 )37-1(

58

L

h

1 h

11 B,H

11 ttB,H

11 nnB,H

2tH

1tH

2nB

1nB

na

ta

22B,H

B,H22 nn

22tt B,H

S

S2

S3 S

1

2

1

2


59/88

( ) ( ) =

+++=

S

1

4

4

3

3

2

2

1L

dSJdLHdLH

h

K )

-: ( LKLHLH 1t2t

L ( ) :-KHH 1t2t = (62 a - 1)

-: K/B/B 11t22t = (62 b - 1)

. K) (

-: )62a - 1( KHa =n (63 - 1)

.

9-3-1-: )Inductor(

m .)Inductance(L

:-

HI/L mL= (64 - 1) mL I.

)44-1(

:-BLIF =

JVHBBLHBLILF 32 ===

V .-: )33-1(

59


60/88

==V

2m dV2

1IL

2

1W HB (65 a - 1)

-: Wm

JdV2IL2

1W

V

22m

== H (65 b - 1)

-: )65a - 1(

FdVI

1L

V2

HB = (66 - 1) V . )65-1(

32

m m/J|21

21w |HHB == (67 - 1)

)64-1()66-1( )38-1( B

I1 .B1B2 B4B3

. B1B2 L1

B3B4 L12 L21 .

:-)38-1( I1 I2B.

)39-1( ) :-23-1(am/H0 I b

m/H0 I- .

60

I2

I1

I2

B1

B2

B3

B4


61/88

m/H0

.

:-)19-1( ab.

:- .

z

a

. ar0 :-

2

2

1

SL

1a

rIHr2 == dSJdLH

m/Aa2

rIH

21 =

22

01 m/Wb

a2

rIB

=

:-

dzdrdr2

1W

1

0

a

0

2

0

m =

HB

m/J16

I|

4

r

a4

Idzddr

a4

rI

2

20

a

0

4

4

20

42

321

0

a

0

2

0

0

=

=

=

61

b

a

ba

I

I

I

0

0

0

I

11 ,HB

22 H,BI


62/88

m/H8

L16

IWIL

2

1 0i

20

m2

i

=

==

bra > a(.

:-m/AL/IN

m/AL/INK = .)17-1(

L/dzINKdz =

:-2

2/322

2

z m/Wb)az(L2

dzINadB

+

=

:-2/L

2/L222

22/L

2/L2/322

2

z |az

z

a

L

L2

INa

)az(L2

dzNIaB

+

=

+

=

62


63/88

2

22z m/Wb

a4L

INB

+

=

) :-40-1()a( L a N

I (b( L/INK =.

L >> aLa4L 22 +

2

z m/WbL/INB =

:-

L

02222/322

z2L

0

z |az

z

a

L

L2

IN

)az(L2

dINaB

+

=+

= 2

22zm/Wb

L2

IN~

aL2

INB

+

=

)64-1(

2mL a)L/IN( = Wb

63

(a)

(b)

snrut - N

a

z

I I

(0,0,z)

B x

zd

L

y

L/IN=K


64/88

N 22

mt a)L/IN( = Wb-:

Ha)L/N(I/L 22

mt==

N )Toroidal Coil())41-1 ) :-25-1( a r0

0r .

:-)41-1( N m/H0r .

:- )41

-1(0r2L = :-

Hr2

aNa

r2

Na

L

NL

0

222

0

22

2 =

=

=

B - H10-3-1-: B H

( ) HB = . BH 0= 0 .

BH .

L/INH 0r2L= .

64

a

B

r0

I

I

0 r

N


65/88

)42-1( BH B .

. I = 0H =0 B

= 0 H H HB

HB .

H B H

. HHmax) H(maxBB =

maxHH > B 0) ( )43-1(B - H (B -H Curve( )Hysterics Loop(. H

Hmax BH 4-3-2-1 5-4 .H B

.)Br( )Br(Residual

H )Coersive)-Hc .H-HcB

. BH 7-6

.maxBB -HmaxH 5- = H-Hmax

BH 8-7 10-9-8 .10-9-8-7-6-5-4

. B - H

.))Hystresis Loss

65

r0

B

I

R

V0

IN


66/88

) :-42-1( BH.

) :-43-1(B - H.

BrHc . Hc

.Br Hc

.

B-H .

66

Bmax

-Bxam

-Br

Br

H c

hr

-Hc

hr

-Hxam

hr

Hxam

hr

`

`

H

h

r

B

h

r

H-B


67/88

. 0 B - H .85 96

+ 10-9- . B- H 8-7-6-5-4'44 '77 .-3-2-14 0

.

))Magnetic Circuits 11-3-1-: Vb)(

R1 R , R2 ,) ( )44a - 1( .)

... ( .

Vb R I .)44b - 1( N I

)WbBA(m = .N I )Reluctance(

m )44c - 1( -:.

VRIVb AR/VI= b=( )

==)A/(LI/VR

b

)44c - 1( :-AIN m = (67 a - 1)

Wb/INm = (67 b - 1)

( ) 1m H)A/(L)AH/(HL/IN=== (67 c - 1)

(I

m

bVIN

R ( .

.

67

N I

m

r0

B

I

N

A

R

I

Vb

(c) (b) (a)


68/88

:-)44-1()a( )b( N)c( .

10cm ))54-1 ) :-26-1( 10cm2 2mm

m/H1000 0 100 10A

mB ) .( .

:- c g

)45b - 1(

1544

32

c H1098.410101041000 10210102AL

= ==

1547

3

g H1092.151010104

102

=

=

)2mm( 62.63mm . )( )

-: ).

mWb48.010100IN

cgm =+

=

=

gB2m

g m/Wb48.0AB =

=

68


69/88

) :-45-1()a( )b( .

)26-1() :-27-1( 2m/Wbm10

.

:-

c

g m Wb10101010 533m ==

A21.0N/I/NI mm ===

:-4-1

Eq-: q

Nq EF =

m 2s/ma

:-

2

2

td

dm

dtmmq

xdvaEF ==== (68 - 1)

69

10mc

B01A

001

01

mc 2

2mm

g

HM 95.1= 1-

0001nruT-A

-

m

c

HM 894.0= 1-

(b) (a)


70/88

a m/s2 v m/s x x) (m.

)46-1( )68-1( .

)Oscilloscope( () )Cathode(

.))Anode )68-1( e

aE me =

x1x2 :-

12

2x

1x

x

2x

1x

VeedxmW === dxEaa

12x2x

1x

Vedxdt

dmW == av

dt

dxv 12=

21

22

2v

1v

Ve)vv(m2

1dm = vv

V0 :-

S/mV109.5m

Ve2v 0

50 ==

dL I ( ):-

BJBdLF == dVId

70

xFqm0

E

) :-64-1( qm E.


71/88

:-vJ v=

:-BvdqBvF == dVd v

:-BvF = q (69 - 1)

)69-1( m kg :-

dt

dmq

vaBvF === (70 - 1)

a v )47-1( B.

x0V av =

t = 0 2z0 m/WbB aB = ( ))70-1

q Cm kg( . )70-1( :-

=

zzyy

xx

o

zyx

zyx

vv

v

dt

d

q

m

B00vvv

aa

aaaa

(71 - 1)

71

qx

z

y

R

F

) :-74-1(q m

0 = t.


72/88

(m/)dtdv v z0B(B q aB =(

:-

dt

dv

q

mvB x

y0 = (72 a - 1)

dt

dv

q

mvB

yx0 = (72 b - 1)

dt

dv

q

m0 z= (72 c - 1)

-: )72c - 1( s/mvv z0z = (73 - 1)

z0v za za . )

72a - 1()72b - 1(vxvy

dt

dv

q

mv

m

qBB

dt

dvB xx

00

y0

=

0vdt

vd

x

2

2

x2

=+ (73 a - 1)

0vdt

vdy

22

y2

=+ (73 b - 1)

m

Bq 0m2Bq

f 0

= )

.(

x) y( :-tsinBtcosAvx += (74 a -1)

y )72a - 1(tcosBtsinAv y = (74 b - 1)

AB 0x vv 0v= y =

0VA = xy :-

72


73/88

s/m)tsintcos(v yx0xy aav += (75 -1)

|| xyv 0v m)qB/(mv/vR 000 == .

vBqF =

Bvq)R/(vmF 2 )qB/(mvR == 00= . q Cm kg

z0B aB B = x0v av m)qB/(mvR = 00=

Hz)m2/(Bq/vf 00 == . s/mvv xz0x0 aav +=

)48-1(. .

.

) )

.

73

z

R

x

y

za0BB =

: R

xa0v (a)

R

x

yza0BB =

:

zxaa z00 vv +

z

(b)


74/88

) :-48-1( 2

z0 m/WbB aB =)a( 2

x0 m/Wbv av =)b(zz0x0 vv aav +=.

5-1-: +q-q

2h )49-1(. z = 0

. )49-

0z)1 +q .

z =h )

74

z

h

h

y

q

q

xV=0

-V3

-V2

-V1

V3

V2

V1

V3

V . m/H0.

a 30-1-:x y xy

z )0,0,h( ba > bah >>.

:-31-1 )59-1( 100 2cm5m/H1000 0=

mm5.2 .I 2m/Wb5.0. .

) :-59-1( 100 .

85

I

2.5mm

51

mc

01mc 01mc

001

5mc 2


86/88

s/m10 32-1-: x7

0 av = V100 )60-1(.

cm5cm5 cm1 z cm60x =.

) :-60-1( x0v a .

33-1-: 2y m/mWb1B = z cm60x = )61-1(.

) :-611( s/m10 x7

0 av =

2y m/Wbm1 aB =.

86

55mc5mc

z

x1

mc

z1

0V

001V

01 7s/m

0=x 5=xmc

mc 01=x

z

x1

mc

z1

01 7s/m

5mcy

mc 06=x

mc 0=x 2mWb/m1 yaB =


87/88

h > a

q

a

x

y

:34-1- )62-1( 1 2)( 12 > VV0

EV )

.

) :-62-1( V0.VV0

m/CL 35-1-: h EV

.

:-36-1 )63-1( +q E

x y.

87

2

1 V

0V

0V


88/88

) :-62-1( q.

Electromagnetics in Arabic

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Transcript of Electromagnetics in Arabic