0ÖFOÖF

§
§
§
§
§
§
§
§
§
§
§
§
§
§

/èLQLâX


&ÔQJYÂLQKSvWpQJWUuQJFƠDFzFQJKwQKNLQKWWKOQKYFWKsQJWLQOLrQO{F
SKzWWULQUWQKDQKFKQJQK|PSKăFYăQKXFXFXFVQJFRQQJuL7KsQJWLQ
OLrQO{FFYDLWUUWTXDQWUQJvLYÂLVSKzWWULQFƠDFzFQJKwQKQOwvQJ
OFWKĐFv\FKRVSKzWWULQFƠD[ảKLKLQv{L
&FWKLWEÊFFSKQWạWURQJKWKơQJWK{QJWLQOLzQOFSKLFĐVẳW}|QJ
WFVDRFKRFĐWKWUX\QGQWÂQKLX~WKLXTXFDRQKW$QWHQOPWESKQ
NK{QJWKWKLX~}FFDKWKơQJWK{QJWLQOLzQOFQKWOWK{QJWLQY{WX\Q~LQ
%LY~OKWKơQJY{WX\Q~LQWKSKLVạGãQJVĐQJ~LQWáQzQNK{QJWK
WKLX~}FWKLWEÊEằF[KRFWKXVĐQJ~LQWá
1Jw\QD\YÂLVSKzWWULQFƠDNKRDKFNWKXWWURQJOQKYFWKsQJWLQ
OLrQO{FvLKLDQWHQNKsQJFKvtQWKXQOwPQKLPYăEơF[{KD\WKXVQJvLQWâ

FvVÂOWKX\WDQWHQ
Đ
wơLYLEWNẵPWKWKơQJ~LQWáQRFĐNKQxQJWRUD~LQWU}đQJKRF
WáWU}đQJELQWKLzQ~XFĐEằF[VĐQJ~LQWáWX\QKLzQWURQJWKẳFWVẳEằF[
Q\FK[\UDWURQJQKQJ~LXNLQQKW~ÊQK
wYÂGãWD[WPWPFKGDR~QJWK{QJVơWSWUXQJFĐNÂFKWK}FUWQKƠ
VRYLE}FVĐQJ+QKD
1X~WYRPFKPWVằF~LQ~QJELQ~êLWKWURQJNK{QJJLDQFDWãV
SKWVLQK~LQWU}đQJELQWKLzQ1K}QJ~LQWU}ÔQJWURQJQ\KXQK}NK{QJEằF
[UDQJRLPEÊUQJEXFYLFFSKQWạFDPFK'ÔQJ~LQGÊFKFKX\QTXD
WãWKHR~}đQJQJQQKWWURQJNKRQJNK{QJJLDQJLDKDLPWãQzQQxQJO}QJ
~LQWU}đQJEÊJLLKQWURQJNKRQJNK{QJJLDQ\&ÔQQxQJO}QJWáWU}đQJWS
WUXQJFK\XWURQJPWWKWÂFKQKƠWURQJOÔQJFXQFP1xQJO}QJFDFK
WKơQJV~}FERWRQQXNK{QJFĐWêQKDRQKLWWURQJFFFXQGy\GQY~LQ
P{LFDPFK
DE
FG
+QK
1XPUQJNÂFKWK}FFDWã~LQQK}KQKEWKGÔQJ~LQGÊFK~}F
ELXWKÊWURQJKQKYWUQJYLFF~}đQJVằF~LQWU}đQJVNK{QJFKGÊFKWURQJ
NKRQJNK{QJJLDQJLDKDLPWãPPWESKQVODQWƠDUDP{LWU}ÔQJQJRLY
FĐWKWUX\QWLQKQJ~LPQPFFK[DQJXâQQJXâQ~LQWU}đQJOFF~LQWÂFK
ELQ~êLWUzQKDLPWã~LQ
1XPUQJK|QQDNÂFKWK}FFDWã~LQQK}KQKFWKGÔQJ~LQGÊFK
VODQWƠDUDFQJQKLXYWRUD~LQWU}đQJELQWKLzQYLELzQ~OQK|QWURQJ
NKRQJNK{QJJLDQEzQQJRLwLQWU}đQJELQWKLzQV~}FWUX\QODQYLYQWơF
QKVQJ.KL~WWLPWNKRQJFFKNK[DQJXâQFKảQJVWKRWNKƠLVẳUQJ
EXFYLQJXâQQJKĂDONK{QJFÔQOLzQKYLFF~LQWÂFKWUzQKDLPWã~LQQD
7KWY\QXWD TXDQ VWFF~}đQJ VằF ~LQ WU}đQJ JQ Wã~LQWKWK\UQJ
FKảQJNK{QJWẳNKSNÂQPFĐ~LPEWQJXâQOFF~LQWÂFKWUzQKDLPWã~LQ


~}F~W
WURQJWU}đQJFDPWVĐQJWUX\QWLWKHRJĐF~ơLYLWUãFFKQWạFĐYFW|~LQ
WU}đQJ(QPWURQJPWSKQJWLKQK
+QKFKLXFDYFW|~LQWU}đQJOzQWUãFFKQWạVO
L
OYFW|~|QYÊWKHRK}QJWUãF] +QK
1XNKLX (
OF}đQJ~~LQWU}đQJFDVĐQJWLWyPFKQWạWK~LQ
WU}đQJWLSWX\QWL~LPFĐWăD~]WUzQFKQWạVO


==
jkzcos
0
z
jkzcos
0
z
e
.
sin
.
E
i
.e
EE

0
0
sin
2
kl
cos
)
cos
2
kl
cos(
2
kl
sin
1
E
e

1X~XYRFKQWạ~}FPFWLWKWURQJWLV[XWKLQGÔQJ~LQ
&{QJWKằFWÂQKGÔQJ~LQ~XYRO




+
=
+
=
2
v


z
i
.
E E
=

(
(
H VằF~LQ~QJ~XYR
(
F}đQJ~GLQWU}đQJWLWyPFKQWạ
= WUNKQJWL
=
WUNKQJYR
O ~GLPWQKQKFKQWạ
N KVơWUX\QVĐQJN




9\TXWUQKWKXVĐQJ~LQWáOTXWUQKFKX\QKĐDQxQJO}QJVĐQJ~LQ
WáWURQJNK{QJJLDQWKQKGÔQJFDRWQFK\WUzQJQKDQWHQ
&QJVXơWFFLWUQWLDQWHQWKX

w[F~ÊQK~}FKLXTXFDDQWHQWKXWDWPF{QJVXWWKX~}FWUzQWLPF
FẳFDQWHQ
*ăLWUNKQJWLDQWHQWKXO
=
5 L;



,
GÔQJ~LQFK\WUzQWLDQWHQWKX
H
QJXâQVằF~LQ~QJFDDQWHQWKX
=
=
,
O
+QK
=  WU¯NKQJYRF´DDQWHQWKX
 7KD\YRWDF§

)
4
.
1
(
R
Z
Z
e
2
1
P
t
2
v
t

2
t
2
o
max
thu
==

5
WKQKSKQ~LQWU¯WKXQWURQJ= 
Đ
&|FWKDPVFĐDDQWHQ
+PSKQJKẽQJ
+PNK{QJFKXQKPQ\ELXWKÊJLWUÊWX\W~ơLFDF}đQJ~WU}đQJ
ằQJYLJĐF

Y

[F~ÊQKQR~Đ
I



(




+PFKXQOWắVơFDF}đQJ~WU}đQJWLPW~LPEWNẵYLF}đQJ~
WU}đQJWLPW~LPFĐJLWUÊPD[+PQ\FKFĐWÂQKFKWW}|QJ~ơL






DEF
+QK

+LáXVXơWFểDDQWHQ
+LXVXWFDDQWHQOWVơJLDF{QJVXWEằF[YLF{QJVXWWRQEP
DQWHQQKQ~}FWáP\SKW~}DWL

0
P
P

=

03
3

3
3

F{QJVXWEằF[FDDQWHQ
3
F{QJVXWYRDQWHQ
3
F{QJVXWWêQKDRWUzQDQWHQ


KRFFSVRQJKQKFĐVẳWêQKDRQKLXK|QGR~ĐKLXVXWWKSK|Q
+áVấQKKẽQJ
w ~QK JL WÂQK K}QJ FD DQWHQ QJ}đL WD GQJ NKL QLP K Vơ ~ÊQK
K}QJ+VơQ\~FWU}QJFKRNKQxQJWSWUXQJQxQJO}QJ~LQWU}đQJYPW
KXQJQR~Đ
+Vơ~ÊQKK}QJOWVơJLDEQKSK}|QJF}đQJ~WU}đQJPWK}QJ
EWNẵYLEQKSK}|QJF}đQJ~WU}đQJWUXQJEQKYLWWFPăLSK}|QJ

()
)
8
.
1
(
E
,
E
D
2
tb
2

=

(



OF}đQJ~WU}đQJK}QJEWNẵ
(










+QK

&§K}±QJF§
WªQKDR
(

θ


ϕ


(
(

9{K}±QJ
NK{QJWªQKDR
9{K}±QJF§
WªQKDR
6 h
×

i
−=
∫

 7L~LPFS~LQOE·QJG¤QJ,
 ,

()
)
10
.
1
(
z
l
k
cos
k
1
kl
sin
I
2
S
l
0
o
i
−=


sin
0
0
=⇒
=

 WKD\] OY] YRWDF§

()
)
11
.
1
(
kl
cos
1
kl
sin
I
S
0
i
−
π
λ
=


h

sin
cos
1
kl
kl
l
hd
−
=⇒
π
λ

7URQJ~§O
OFKLXGLKLXG·QJF´DDQWHQF§FKQW¹~¬L[»QJ
class="bi x0 y0 w1 h1"
$QWHQFKQWơxL[đQJ

QKQJKắDFKơQWỉấL[QJ
&KQWạ~ơL[ằQJOPWFXWUảFJâPKDL~RQYWGQFĐKQKGQJW\
KQKWUãFKĐSHOLSVRLWFĐNÂFKWK}FJLơQJQKDX~WWKQJKQJWURQJNK{QJJLDQ
YJLDQơLYLQJXâQFDRWQ








3KQEấGQJLáQWUQFKơQWỉấL[QJ



+QK
a

a

O
=
=
+QK
*LVạNKLELQGQJ~}đQJGy\VRQJKQKWKQKFKQWạ~ơL[ằQJWKTX\
OXWSKyQEơGÔQJ~LQWUzQKDLQKQKYQNK{QJWKD\~êLQJKĂDOYQFĐGQJVĐQJ
~ằQJ

()
)
13
.
1
(
z
2
l
sin
I
z
I
b


WÂQKWRQNWKXWFĐWKFKRSKSSGãQJJLWKLWSKyQEơGÔQJ~LQVĐQJ
~ằQJKQKVLQ
7U}đQJKSFKQWạ~WWURQJNK{QJJLDQWẳGR:

WDFĐ
)
14
.
1
(
e
sin
2
kl
cos
)
cos
2
kl
cos(
I
60
i
jkR
0






jkR
b














=


7URQJv,OGÔQJ~LQ~XYRFKQWạ

()






=
2



D- OELzQ~GÔQJWLWăD~]FDFKQWạ
-
OPW~GÔQJ~LQPW
4
O~LQWÂFKPWWUzQPWG|QYÊFKLXGLFKQWạ
*LLSK}|QJWUQK~ơLYL4
WURQJ~ĐWKD\, ELSK}|QJWUQKWDFĐ
0
z
)
z
2
l
(
k
cos
i
kI
Q
0
z
)
z
2
l
(
k
cos



a

DO


DO


DO


+QK


1KQ[W
'ÔQJSKRF~LQWÂFKWUzQFKQWạSKyQEơWKHRTX\OXWVĐQJFK\O
VĐQJGăFWKHRWáQJQKQKFDFKQWạELzQ~NK{QJ~êLQK}QJSKDELQ~êLWKHRYÊ
WUÂ


PôL~LPWUzQFKQWạGÔQJYSOFKSKDQKDX


%LzQ~GÔQJYSWL~LPFSQJXâQSKãWKXFYRWắVơO


&FK~XGy\




5
5 ]FRV


7DFĐG]
EằF[WL0F}đQJ~WU}đQJOG(
a

G
G
]
0
O
O
5
5
5


+QK
)
18
.
1
(
e
sin
dz

2
θ
λ
π
=

95
5 ¯G}±LPXQzQ~W5 
≈
5 
≈
5 
 7DF§
)
cos
z
R
(
jk
1
0
e
sin
dz
I
60
j
dE
θ−
θ

2
l
(
k
sin
I
I
m
−=

 &}®QJ~WU}®QJWªQJO

2
1
dE
dEdE
+=

)
20
.
1
(
)
e
e
(
e
sin
)

)
z
2
l
(
k
sin
dz
I
60
j
dE
m
θθ−
λ
π
=⇒

&}®QJ~WU}®QJWL0O

)
21
.
1
(
e
sin
kl
cos
)

M
1
0
jkR
m
1
0
M
θ
−θ
=
θ−θ
λ
π
==
∫∫

 %LzQ~F}®QJ~WU}®QJWL0O

)
22
.
1
(
sin
kl
cos
)
cos
kl

wâWKÊK}QJFDFKQWạ~ơL[ằQJWURQJPWSKQJNLQKWX\Q(











1KQ[W
9LPWJLWUÊFDWắVơO

~XNK{QJFĐEằF[GăFWKHRFKQWạ
9LO

WKFKQWạEằF[FẳF~LYKDLSKÂD




wâWKÊK}QJ
FDFKQWạFĐGQJKQKVơYFKFĐKDLEảSK}QJFKÂQK
9LO!

EW~X[XWKLQEảSSKãOFQJWxQJWKEảSSKãFQJOQ
EảSFKÂQKFQJJLPFKR~QNKLO





+QK
7URQJ~Đ / O~LQFPSKyQEơFD~}đQJGy\
&
O~LQGXQJSKyQEơFD~}đQJGy\
0WNKFWDFĐ
d
C
LC
C
v
CL

à
àà
=====
1
1
1
1
1
1
4
4
1
1
1
1

)
26
.
1
(
a
D
lg
276
d
=

'NKRQJFFKJLDKDLGy\GQ
DEQNÂQKGy\GQ
&ÔQ~ơLYLFKQWạ~ơL[ằQJKRFFFORLDQWHQGy\NKFWK~LQGXQJSKyQ
Eơ&
~y\NK{QJSKLOKQJVơPWKD\~êLGăFWKHRFKLXGLFDGy\~}FWÂQK
WKHRF{QJWKằF
)
27
.
1
(
)
1
a
l
(ln
120
=

7URQJ~Đ 5

O~LQWUEằF[
3

OF{QJVXWEằF[
,OELzQ~GÔQJ~LQWUzQFKQWạ
7X\QKLzQWURQJWU}đQJKSQ\GÔQJ~LQFĐELzQ~SKyQEơNK{QJ~XGăF
WKHRFKQWạ9Y\NKLELXWKÊF{QJVXWEằF[WKHRELzQ~GÔQJ~LQWLYÊWUÂ
QR~ĐFDFKQWạWKW}|QJằQJVFĐFFJLWUÊFD~LQWUEằF[ằQJYLGÔQJ
~LQ~LP~Đ
1KQ[W
9L O

ẻ5

JăLOFKQWạQạDVĐQJ
O

ẻ5

JăLOFKQWạFVĐQJ
O

WKNKLOWxQJVWxQJVơSKQWạFĐGÔQJ~LQ~âQJSKDGR
~ĐWxQJF{QJVXWY~LQWUEằF[
O

!WKWUzQFKQWạV[XWKLQKDLSKQGÔQJ~LQQJ}FSKD
OPJLPF{QJVXWY~LQWUEằF[FDFKQWạ


OF{QJVXWEằF[
5ONKRQJFFKWáFKQWạ~Q~LPNKRVW
:OWUNKQJVĐQJFDP{LWU}đQJ
(

O~LQWU}đQJEằF[~}FWÂQKWKHRF{QJWKằF

















=
i
R
e
sin
2

YGÔQJ~LQ~XYR,









)
30
.
1
(
jX
R
I
U
Z
v
v
0
0
v
+==

7URQJ~Đ 5
5


)
32
.
1
(
2
kl
g
cot
j
I
U
Z
a
0
0
0
==

7URQJ~Đ
2
kl
sin
II
b
0
=

a
a

R
I
I
R
R
I
2
1
R
I
2
1
2
2
0
2
m
0
2
m
0
2
0



==


5

FẳFQJQ~QVĐQJGLYFẳFGL7X\QKLzQPôLGLVĐQJNKFQKDXFKQWạFàQJ
FĐQKQJ~F~LPNWFXULzQJSKãWKXFYRE}ĐFVĐQJY~F~LPWUX\QODQ
FDGLVĐQJ\
$QWHQFâQ
DiQKQJKD
$QWHQFQOFKQWạFKFĐPWQKQK~XG}LQơLYLP\SKWP\WKX
FÔQ~XNLDFDP\SKWP\WKX~}FQơL[XơQJ~W
E7QKSKonQJKoQJ


O








O


9FKQWạNK{QJ~ơL[ằQJ~WWKQJ~ằQJVWQJD\WUzQPW~WGQ~LQO
W}QJQzQWDWKD\QKK}QJFDPW~WEQJPWFKQWạQK'R~ĐFKQWạWKẳF
Y QK WR WKQK PW FKQ Wạ ~ơL [ằQJ ~W WURQJ NK{QJ JLDQ Wẳ GR 9 Y\ WÂQK
K}QJFDFKQWạNK{QJ~ơL[ằQJ~WWKQJ~ằQJWUzQPW~WVJLơQJQK}WÂQK
SK}|QJK}QJFDFKQWạ~WWURQJNK{QJJLDQWẳGR~[W
Đ

+PSK}|QJK}QJFDPWSKQJNLQKWX\Q(