>^|SK
Electromagnetic Field
oR1∗
∗þ°ÏÆ>íX
)
lixuguang@gmail.com
2009c521F
¥þ©Û )K:
)K:
• ¥þܤک)¶
• ¥þIÈڥȶ
• FÝÑÝÚ^ݶ
• Î¥IXeFÝ^ÝÑÝO¶
• ICÚÈ©C¶
• Fݽn!ÑݽnÚ^ݽn"
oR1 (þ°ÏÆ>íX)
>^|SK
2009c521F
2 / 90
¥þ©Û ~KÀù
~1
• ½¥þ¼êµ
~F = ~ax(3y − c1z) + ~ay(c2x − 2z) − ~az(c3y + z)
• (1)XJ ~F´Ã^|§(½~êc1, c2, c3¶
• (2)¦Iþ¼êV§¦ÙKFÝ ~F"
oR1 (þ°ÏÆ>íX)
>^|SK
2009c521F
3 / 90
¥þ©Û ~KÀù
~1(1)
• Ï ~F´Ã^|§∇ × ~F = 0§=µ
~F =
∣∣∣∣∣∣∣∣∣
~ax
~ay
~az
∂
∂x
∂
∂y
∂
∂z
3y − c1z c2x − 2z −(c3y + z)
∣∣∣∣∣∣∣∣∣
= ~ax(−c3 + 2) − ~ayc1 + ~az(c2 − 3)
= 0
• ∇ × ~Fz70§Ïdc1 = 0, c2 = 3, c3 = 2"
oR1 (þ°ÏÆ>íX)
>^|SK
2009c521F
4 / 90
¥þ©Û ~KÀù
~1(2)
• Ï ~F´Ã^|§7±L«Iþ¼êVFݧÏdµ
~F = −∇V = −~ax
∂V
∂x
− ~ay
∂V
∂y
− ~az
∂V
∂z
= ~ax3y + ~ay(3x − 2z) − ~az(2y + z)
• ddnúªµ
∂V
∂x
= −3y
(1)
∂V
∂y
= −3x + 2z
(2)
∂V
∂z
= 2y + z
(3)
oR1 (þ°ÏÆ>íX)
>^|SK
2009c521F
5 / 90
¥þ©Û ~KÀù
~1(2) (Cont’d)
• úª(1)éxÈ©§±µ
V = −3xy + f1(y, z)
(4)
• d?§ f1(y, z)´dy, zû½¼ê§úª(2)Ú(3)©OéyÚz¦È©±µ
V = −3xy + 2yz + f2(x, z)
(5)
V = 2yz +
z2
2
+ f3(x, y)
(6)
• ©Ûúª(4)(5)(6)±TIþ¼êµ
V = −3xy + 2yz + z
2
2
(7)
• úª(7)\?¿~êVE÷v)§T~êd>.^½öá?>.^û
½"
oR1 (þ°ÏÆ>íX)
>^|SK
2009c521F
6 / 90
¥þ©Û ~KÀù
~2
• ¦¥IXe¥þ|Ñݵ
f1(~R) = ~aRRn
f2(~R) = ~aR
k
R2
oR1 (þ°ÏÆ>íX)
>^|SK
2009c521F
7 / 90
¥þ©Û ~KÀù
~2)
• 3¥IX¥µ
∇ • ~A = 1
R2
∂
∂R
(R2AR)
• XJµ
~A = ~aRAR
• Kkµ
∇ • ~A = 1
R2
∂
∂R
(Rn+2)
= (n + 2)Rn−1
∇ • ~A = 1
R2
∂
∂R
(R2
k
R2
)
=
1
R2
∂
∂R
(k)
= 0
oR1 (þ°ÏÆ>íX)
>^|SK
2009c521F
8 / 90
¥þ©Û ~KÀù
~3
• y²µ
1
3
∮
S
~R • d~s = V
• Ù¥~R´¥IXe¥»§V´4Ü¡S¤NÈ"
oR1 (þ°ÏÆ>íX)
>^|SK
2009c521F
9 / 90
¥þ©Û ~KÀù
~3)
• é¥IXe¥»µ
~R = ~aRR
∇ • ~R = 1
R2
∂
∂R
(R2 · R) = 3
• âÑݽn§kµ
1
3
∮
S
~R • d~s = 1
3
∫
V
∇ • ~Rdv = 1
3
(3V) = V
oR1 (þ°ÏÆ>íX)
>^|SK
2009c521F
10 / 90
>^|Ä 5Æ )K:
)K:
• ðd§|©/ªÚÈ©/ª¶
• ðd§|>.^¶
• ·<˽nÚ·<Ë¥þ¶
• ÅħÚ>^ ¼ê¶
• ²0¿[§¶
• >^|EêL«"
oR1 (þ°ÏÆ>íX)
>^|SK
2009c521F
11 / 90
>^|Ä 5Æ )K:
©½/ªðd§|
∇ × ~E = −∂
~B
∂t
∇ × ~H = ~J + ∂
~D
∂t
∇ • ~B = 0
∇ • ~D = ρ
oR1 (þ°ÏÆ>íX)
>^|SK