2134 Marks 4

2483 Marks 3

1472 Marks 2

10101 Mark 1

=

=

=

=

(1)

(2)

[ ]ATML 02- [ ]ATML -22

[ ]ATLM 0-20

9

8

8

9

6

7

(3)

zeroF=

Rays-a Rays-b

RaysX -

BSinè qF J= B qF J=

Raysg=

BA+ BA+BA. BA.

(4)

(5)

W 6

W 6

W 21

W 21A S B

mhoOhm

1

impedance

1===

(1)

o oA AC C'

d 2d

E E= =

[ ]ATML 02- [ ]ATML -22

[ ]ATLM 0-20

zeroF=

[ ]ATLML

A

A

IJ 020 -Þ==

Sinè BqF J=

Sinè BqF J=

BqF J=

J

(2)

9

8

8

9

6

7

4

3a w

w

a

nn

n==

3 3 9

22 84

3

g ga wg g

a w

n nn n

n n==Þ===

Rays-a Rays-b

RaysX -Raysg-

BA+ BA+BA. BA.

(3)

18103 -ms

kgmJSh 3134 101.9 10625.6 -- =´=

Ce 19106.1 -=

(4)

A i ed+=+

0 0 030 30 60 0

e A i

e

d=+-

=+-=

0

0

0

30

60

30

?

A

i

e

d

=

=

=

=

Þ

h

ml

J= 1

eVmv

eVmv

2

2

1

2

2

=

=

meVmv

meVvm

2

222

=

=

1

2

h

meVl=

34 10

31 19

6.625 10 12.27 10

2 9.1 10 1.6 10m

VVl

- -

- -

´ ´= =

´ ´

012.27 or A

V

' 'J

84

3

3 102 10 20

15 10

cm or kml

J

´== =

´

120 5

4km km= =

2

1

la

l

Rhd 2=

Rd a

hd a

(5)

(6)

l

l2

- q

A

+ q P

OB

l l 1E2E

r

1 20

4 ( )

PA r l

qE

r lp

=+

\=Î+

1 20

qE PA

4ð APAlong\=

Î

1

2

BP r - l=

Along BP Produced2 2

0

4

qE

BPp\=

Î

2 204 ( )

q E

E r lp\=

-

2 1E=E -Eururur

2 20 04 ( ) 4 ( )

q q E

r l r lp p= -

Î- Î+

2 20

1 1

4 ( ) ( )

qE

r l r l

é ù\= -ê úPÎ- +ë û

2 2

2 2 20

( ) ( )

4 ( )

q r l r lE

r lp

é ù+--=ê ú

Î-ë û

2 2 2 2 2 20 0

4 2 2

4 ( ) 4 ( )

q rl q l rE

r l E r lp p

é ù ´= Þê úÎ- -ë û

2q l P=ur

2 2 20

2

4 ( )

P rE

r lp

´=

Î-

urur

204 ( )

q

r lp=

Î+

[]1o eE E H=+

1oe

EH

E=+

(7)

4 30 0

2 2

4 4

P r PE or E

r r

´\= =

PÎ PÎ

ur urur ur

l r<<

3

1 or E

ra

ur

andss+-

0Eur

0 0E E E=-ururur

PE

s

s

o p o

o

Por E E E E E

E

s+=+Þ=

Dielectric constantoEK

E

é ù=ê ú

ë ûQ

e oo

o

H E EE E

E\=+

o pE E E=-ururur

[ ]p P Polarisation vectors=Q

o

o

PE E

E\=+

e oP H E E=

pE

3 \ eqn

2

1

2

3

1

2 V Kl\=®

1

2

lE

V l=®

1E

r RV

æ ö=-ç ÷è ø

(8)

Constant I

KA

d=

l IV I V l

A A

dd

æö\=Þ=ç÷

èø

lR

Ad=

V Kl=

or v la

A

A B

RhK1

J 1J

K2

+

R

G

1AJ l=

1 12J and AJ =l

1E Kl\=®

1

2

1l

r Rl

æ ö=-ç ÷è ø

(9)

W 6

W 6

W 21

W 21A S B

1 1 1 2 1

18 18 18 9pR\=+==

9Por R =W

W6 W12

W=+18126

W6 W12

1 1 1 2 1 3 1

6 12 12 12 4pR

+\=+===

4PR\=W

4W4W

8Ù44Req. =+=\

(i)

RP

QS

S

R

Q

P ÷

ø

öçè

æ=Þ=\

1 g 1I P I G (I I )R 0+--= []0Ig =Q

1 1 I P (I I )R\=-

1 1 I P-(I I )R=0-

B

P

K

C

S

D

R

GA

)I(I Q g1 -

1 (I I )-

Ig1I

1 g (I-I +I )

(10)

1 g 1 g g(I -I )Q (I-I I ) I G 0d-+-=

1 1I Q=(I-I )S

[]0Ig =Q

0)SI-(IQI 11 =-

(ii)

P R

Q d=

I

I

Qr

C

P

B

A

dl

dB

2

(i) dB d

(ii) dB á l

(iii) dB á Sin

l(iv) dB á

r

la

q 2 2

Id Sin KI Sinè dB á dB

l dl

r r

q\ Þ=

0uK

4ð

é ù=ê ú

ë ûQ

02

Id Sinè. dB

4 r

u li e =

P

I

I

R

C

A Bdl

r

dl r dldl == 00 Sin90 90

024

u IdldB

Rp\=

02

ˆu Idl rdB

4ð R

´=

uruur

0 02 2

24 4

u uI IB dl R

R Rp

p p= Þò

0 2

4

u IB

R

pd

p\=

(11)

0 2

4

u nIB

R

p

p\=

0. u Ii e B. dl =òuruur

SN

II

B

D

A B

C

l

0 0Cos90 Cos90 0C A

B D

B dl B dl\ = =ò ò

)(i

ò=D

C

dlB 0 .

( )ii

òòòò ò +++=A

D

D

C

C

B

B

A

dlBdlBdlBdlBdlB .....\

òòò ===\ BldlBdlCosBdlBn

A

00 .

BHQ

BE

BV

MagneticMeridian

Geographic Meridian

d

(12)

( )iii0= u nlI

0 0U B U nI Since N

Bl nlI or nl

= = =

0u NIB

l\=

d d

H E

V E

B B Cos

B B Sin

d

d

=

=

(i)

(ii)

2 2 2

2 2

H V EB B B [Sin Cosdd+=

2 2E H V B = B +B\

V

H

Btan

Bd=

×net current in loop ABCDuodlB =ò.

fo M.P

fe\=

-

for M.P

feo =

(13)

â , áa

b

tan

tanM.P =

M.Pb

a=

B'C

B'A'tan

2

=b

B'C

B'A'tan

1

=a

B'C

B'C

B'A'

B'C

B'C

B'A'M.P

2

11

2

=´=

a

J

1C B' fo=

2C B' = fe-

O

E

C2

C1

Fo

B

1A

Fe

I

1B

aa

aa

2 20 0

2 2 2

h 4ð E h Er or r

4ð m e m ep= =

20

2

4

1

r

Ze.e

Eðr

mv=

(i) r

kze

r

mvor

2

22

®=

(14)

0

1

4Where k

p=

Î

h nh(ii)

2 2ie mur

p p®

2 1 f ih E E or E EJ=- -

2 22

2 2

n hr or

4ð m kZer na=

(ii) eqn

nh

2ð mrJ=

2 2 2

2 2 2 2

m n h kZe

r 4ð m r r=

2

2 20

h 1r

4ð m ke 4k

Ep= =

oI I Sin wt=

J

2 H Ir.ms . RT\=

22 OI ms.RT

Ir.m.s RT2

\ =

OO I 0.7072

IIrm.sor ==

(15)

T2 2

o

O

dH I RSin wt dt=òò

2 2 2OdH I Rdt I Sin wt Rdt==

T2 20

O

H=I R Sin wt dtòT

2o

O

1-cos2 wtH I R

2dt

æ ö=ç ÷

è øò

T T2O

O O

I RH dt - Cos2 wt dt

2

é ù=ê ú

ë ûòò

2 1 Cos2 wt Sin wt

2

-é ù=ê úë û

Q

2oI R sin2 wt

H= T-2 2w

é ùì üí ýê úî þë û

20OI R 1 2

H Sin 2. . Sin2 2

T T ow T

pé ùì ü= - -í ýê ú

î þë û[ ]0SinoSin4ð 0 ==Q

2

RTIH

2

O=

1

2

3

S

T

o

d

S1

S2

P

A

O

B

y

D

tvAD 2=

-Ð : ÄABC ed

ed ÄADC :Ð -

2v tADSin r (iii)

AC AC== ®

1 1

2 2

v tSin i AC =

Sin AC v t

v

r v=

1v tBCSin i (ii)

AC AC== ®

-:(i) eqn

rSin

iSin nor

v

vn

2

1 ==

2n1

2

vn = (i)

v®

(16)

n1

V1

V2

B

t

t Cri

D

A

2v t

tvBC 1=

= 42 2

yd dyx

D DD =

(17)

PSPS Ä 12 -=x

1/22 22 2S P= S B +PBé ùë û

2rt. ed Ä S BP:-Ð

1/22

22

dS P = D + y+

2

é ùæöê úç÷

èøê úë û1/22

2 2

dy+

2S P =D 1+

D

é ùæöê úç÷

èøê úê úê úë û

2

2 2

dy+

2S P =D 1+ (1)

2D

é ùæöê úç÷

èøê ú®ê úê úë û

2

1 2

d1+ y

2S P =D (2)

2D

é ùæ ö-ê úç ÷

è øê ú®ê úê úë û

2 2

2 1 2 2

d d1+ y+ y

2 2S P -S =D 1

2 2x

D D

é ùæö æ ö-ê úç÷ ç ÷

èø è øê úD- --ê úê úë û

2 2

2

D d d= y+ y-

2 2 2x

D

é ùæöæöD -ê úç÷ç÷

èøèøê úë û

mëD

yd=

d

Dmë=y

d

Dy 1m 1

l==

0m 0 y 0==

1 0

Dëy y

db=-=

Dë

db=

(18)

IC

E

BC

VECRL

VO

npn --

(i) III cbe ®+=

(ii) RIVECV LCo ®-=