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Bài giải Trường Điện Từ

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 ' $-
.'
π
 
 
× =
 ÷
 
 
 


PHN 2: NI DUNG
Câu 2.1 !"#$%&' ()$*+,
/01$ 23'  ,. 45#6789(

:; 5/<$:" 23
=>

?' 5 ,5@ !8ABCDABECDAEBCAEBECFGH 23IJ
 !" !<* ,@ !8*

B%5#K:,FLI;M2$"9(
:; !" 23IJ%0+$ !N$+ !<*IJ#$#:O:;P
 5/<$:" 23

1 1 .1 1


[
v %" " " " &
 l
= + + +
πε
r uur uur uur uur

-
1 1 .1 1

%" " " " &  

+ + + = =
uur uur uur uur
  

  

  % &
 
  %$1  & $
 
o
q
F
d
πε π



= × = × = ×
× ×

Câu 2.2.  

Bµ'  ,$ Q.

Bµ'  ,4
RABDEBDC78STU54 !"' ()$*6 (OM&:; 5
/<$:"


Giải
54 !"' ()$% Q.AMBHBC

 T.' *"FV W!X(01$
Y


Z

:[

M
M
H
H
BV W!X(01$ Y

Z

:
[

AM\BC
M
AHBC
H
]9(:; 5/<$:"


.  .  .
.
.
.
.
.

o

Q Q R Q R
F
R
R
πε
 
 
= +
 
 

( ) ( )
( ) ( )
'
.
$1
  $1
 
$ $ $'
$% &

 % &
$ $'
x y
x y
o
x a y a
xa ya
Q
x y

x y
πε

 
 
− + +
+
×
 
 
= +
 
+
 
− + +
 
 
 

WM 09
( )
( )
( ) ( )
$1 $1
  
$ $
$

$ $'
x

x
x a
xa
x y
x y
 

 
= +
 
 
+
− + +
 
 
 


]W'
( ) ( )
$1
 
   $1
$ $' %$ & % &x x y x x y
 
− + + = − +
 

Câu 2.3:W'  ,RABBCBAEBBCBABBCB^ABEBC !W$6_$
$7L9(:; 5/<$:"R

Giải
]9(:;IJ#$
- 
. . .
%1  &

CA
DA A
o
CA DA BA
R
R R
F
R R R
πε

 
×
= + +
 
 
 
B

`
2 2 
CA x y DA x y BA x
R a a R a a R a= − = + =
. Độ lớn
2 $

CA DA BA
R R R= = =

7HW_$ 2 !" 09
( )

-
1 
  
$1
 
   
x x
o
F a a N
µ
πε

×
 
= + + =
 
 

Câu2.4:
W


µ
'  ,a


ABBC

E
µ
'  ,a

ABBCW

εε
=

a/7Lb


c; 5/<$:"

:
( ) ( )
( )
' '
  

.
$1

  1   
% $1 $ &
  '
x y

x y
o o
a a
Q Q R
F a a mN
R
πε πε
− −
× − × +
= = = − −

b/7L Q.&a

ZT$>Id9(:; 5/<$:"

#$
7%

.  .  .
. .

. .

Q Q R Q R
F
R R
πε
 
= +
 

 
 
AC
F+[

AM\C
M
AHEC
H
[

AM\C
M
AHEC
H
7TH">#(> !"
. 0e$ )$@ !8

IJ/Q VWV 1[

6fW/ +


?./&[


1$
&'%
&11%
=



g$  hH

% Q.AMBMBC
7HWAC 09
( ) ( )
( )
( )
( )
.
 $1
  $1

 
  $1  1 ' $1% '&

z  $1 % & {
' $1 % '&
x y x y
o
x a x a x a x a
Q
F
x x
x x
πε
 
   
− + − − + −

 
   
= −
 
− + −
 
− + −
 
 
 

7HiT6i#WAb

CB 09
{&&%&1$&z%%'%1{&'&%&1$&z%%%
1$1$
=−+−−−+−
xxxx
[g $Q 09

( )

'−x
\
( )

−x

]W'
$

.
.'
=


=x
FGH Q.&a

:ABBC
Câu 2.5: W


nC
'  ,a

ABEBC

 ,
a

AEBBEC
a/jZT

εε
=
Bkl ,a

ABBC

? !0e$l ,a


:
-
. .
. .
. .
1 '


o
R R
E
R R
πε

 
= +
 
 
 

F+[


  
." " "− + −
[


  

" " 1"− +
r r r

mTH!
1
..
== RvàR
7HW_$ 2 !" %
( ) ( )
-
$1 $1

1 .   '   1

  1
x y z x y z
a a a a a a
E
πε

 
× − + − × − +
= + 
 
 


M
E
H


*
b/7L4 !" !<nl
M
o
a% Q.ABHBCB[

E
( )
zyx
aaya  −++

( )
zyx
aayaR .
.
+−+=

( ) ( )

.

.
.'1
−+=++=
yRvàyR
? !0e$l
M
 ,4a:
l

M

( )
( )
[ ]
( )
[ ]






+
−+
×
++
−×

1$

1$


-
.
.'
'1
1



yy
πε
7%l
M
B HW#4T 2 09
H

H
mTH!HEBHEB
Câu 2.6 :?4n'  ,RABBCABBEC !W$6_$$ ;/W
a.7Ll ,aABBC

-
. .
 

AP BP
p
o
AP BP
R R
E
R R
πε

 
×
= +
 

 
 

F+[
Ra

$
1$
zxBPzx
aavàRaa +=−

1$==
BPAP
RR
-
$1
 
 E
 $1
x
p
o
a
E V m
πε

×
= =

b.? ,$ Q.#$#W"TojZT !0e$ ,Q4iT#$T

L


 $1
o
o
Q
πε
=

mTH!



Câu 2.7: 4
C
µ

'  ,4RABBC !W$6_$$7LlpBlqB
l
*
 ,aABBC
7%
' '
.
$1
 - .
   
'1$- $. -
  '

x y z
AP
p x y z
o o
AP
a a a
R
E a a a
R
πε πε
− −
+ −
 
× ×
= = = + −
 
 

7,4a
568
$

=+=r
B

.$1'&E%" ==

φ

zz =

7Y% %
 
'1$-% $ & $.% $ & '1$-b%1'$. & $.b5%1'$. & 1-$
P P x y
E E a a a a a
ρ ρ ρ
= = + = + =
 
$ '1$-% $ & $.% $ & '1$-b5%1'$. & $.b%1'$. & $
P x y
E E a a a a a
ϕ φ φ φ
= = + = − + =

$-−=
z
E

câu 2.8: W4%.:+#$
C
µ
−
'  ,4
&1$22%

P

&1$22%

−P


F. %.:+
C
µ

'  ,$ Q.
7L0e$. !0e$l ,4aABBC !W$LOT$>Id

εε
=
Giải
0e$. !0e$l ,4a:
'
.
 
. . .
  .


p
o
R
R R
E
R R R
πε

 

= + −

 
 
 

+R

, R

, R

:5V W!:O:09 MTh (5  Ya

Ba

Ba

 +a
7%

%22$1&R =
B

%22&R =
B
.
%22$1&R =
F.:+:
'$

=R

B
$

=R
B
1$
.
=R
^W%
zyP
aaE $ $-
&1$%
&1$22%
&$%
&22%
&'$%
&1$22%




'
+=






−+


=

πε
7,4a %
1=r
B

2'.&1E%b ==

θ
B

-=
φ
FLGH %
-$'b$-b5b5-$-&$%$-&$%-$- =+=+==
θφθ
rzryrPr
aaaaaEE
1$&b5%$-b5b-$-&$%$-&$%-$- −=−+=+==
θφθ
θθθθ
aaaaaEE
zyP
b-$-&$%$-&$%-$- ==+==
φ
φφφφ
aaaaaEE
zyP

Câu 2.9: 4%.:+
nC
'  ,4RAEBBC !W$6_$$7L
STU4aAMBHB*C ,%
mVE
x
E1=

Giải
a)0e$. !0e$ ,aIJ:

-

 

AP
P
AP
R
E
R
πε

×
=
B  F+ 
% & % & % .&
AP x y z
R x a y a z a= + + − + −
B  F .  :+ &  V W! R

Ra
 :
E
  
% & % & % .&
AP
R x y z
 
= + + − + −
 
7(O !0e$ VW !<M:
[ ]
1
&.%&%&%
&%


1$


-
=









−+−++

=

zyx
x
E
x
πε
AFrC
F0GHIJ !s 
[ ]

&.%&%&%1'$&% −+−++=+ zyxx
b) 7L

y
ZT
&.22%

yP −=
 !"STU7,4a %
.

{&%z-$. −+= y
7Y%
$&%


=−y

H
'-$

=y
W'
Câu 2.10 :?EZ'  ,AEBBCABBC 01$2$Z 

∈=∈
M5
@

 ,aABHBC
Giải
? !0e$ ,a:
-
 
. .

 
l l 


l l
p
π

 
×
= −
 


 
 
7,

l
:V W! YAC +4a:AEBHBC ,

l
:V W! Y
A\C +4a:ABHBC?.:+&t$V W!

 
l l - y= = +
4T 2

p
T9
TH4u 
-
 $1

'
 

 %- &
x
p
a
y

π

 

×
=
 
∈ +
 


×