Electromagnetic

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Electromagnetic

• ???? ?????????
• kvkasin_at_kmitl.ac.th

2
(from Lawrence Livermore National Lab)
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(From Dr. Ulabys Book)
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(From Dr. Ulabys Book)
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Model of Electromagnetic Systems

• ?????????????????????????????????????????
• ???????
• ????
• ?????? ??????? vector, ??????????????? scalar
• ????????? Emag
• ??????????? scalar ?????????????? Q ????? I
• ??????????? vector ???? ????????????????? E
• ????????? ??????? ????????? Emag
  ????????????????????????????????????????????
  ???????????? vector ???? scalar
• ??????????????????????????????????????????????????
  ?????????????????????????????? ?????????

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Vector Analysis/Coordinate System

• ????????????????????? 3 ???
• ??????????????????????? (Cartesian coordinate)
• ?????????????????? (Cylindrical coordinate)
• ??????????????? (Spherical coordinate)
• ???????????????????? ????????????? orthogonal
• ????????????????????????????????????????????????
• ??????????????????????????????????????????????????
  ??????
• ??????????????????????????????????????????????????
  ?????????????????????????

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Vector Algebra

• ???

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Vector Algebra

• ??

• ???

• dot product

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Vector Algebra

• Cross product

?????????????????
(1)
(2)
???????????????????????????????????????? A,B,C
(3)
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?????????

• ??? ??????????????????????
• ??? ?????????????????????????????
• Orthogonal Coordinate System
• ?????????????????????????????????????????????(surf
  ace)??????????????
• ?????????????????????????????
• ?????????????????????????????? ???????????????
  ??????? ??????? ?????????????? ??? ???? ??? ????
  ????? ???????

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???????????????????????

• ??? P (x1,y1,z1) ??????????????????? ????? x
  x1, y y1, z z1 ?????????????????
  (??????????????????) ????????? origin ?????? unit
  vector ??????????????? x1, y1, z1

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???????????????????????

• ???? x1, y1, z1, ???????????? vector ????????
  ??????????? ???????? base vectors
  ??? ???????????????????????
• ??? P(x1,y1,z1) ?????????????????
  ?????????????????? ????????????????? base vectors
  ????

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???????????????????????

• ???????? ????????????????????????
• ??? ?????????????????????????
  (origin)????????? ????????????? ????????
• Dot product
• ???

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???????????????????????

• Cross product
• Differential length ?????? dx, dy, dz
• Vector differential length

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???????????????????????

• ????? P1??? P2 ???????????
• differential volume dv dxdydz

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???????????????????????

• ???????? ????
  ????????????????????
• ?????? ???????? z
• ???????? ??? z ????????
  ??????????????????
• 
  Ans

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??????????????????

• ?????????
• ??? P ??????????????????????????????????????
• ??????????????????????????????? z ??????????
  r1????????? z
• ???????????????????????????????? z ????????
  1????????? x
• ??????????? zz1

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??????????????????

• ?????????
• ??? P ????????? P(r1, 1,z1) ???
• Base vectors ????????????????????????
  ??????
• Differential length (????????????????????????????)
  
• Scalar
• Vector

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??????????????????

• Differential volume
• Differential surface

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??????????????????

• ???????? ??? P (3, , 5) ????????????
• P (r, , z)

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??????????????????

• Transform ??? (r, ,z) (x,y,z)
• ??????????
• x rcos
• y rsin
• z z
• ???????????????
• Ax
• Ay
• Az

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??????????????????
????
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???????????????

• ?????????
• ??????????????????????
• ????????????????????? R ????????? origin
• ???????????????????????????????????? z
• ???????????????????????????????? ????????? z
• Base vectors ????
• Differential length
• Scalar
• Vector differential length
• Differential volume

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???????????????
?????????????
25
???????????????

• Transform to (x,y,z)