전자기 포텐셜과 맥스웰 방정식

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개요

• 벡터포텐셜 \(\mathbf{A}=(A_x,A_y,A_z)\)
• 전기장
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  \(\nabla \cdot \mathbf{B} = 0\)로부터, \(\mathbf{B}=\nabla \times \mathbf{A}\)
  
• 스칼라 potential \(\phi\)
  \(\mathbf{E}=-\frac{\partial\mathbf{A}}{\partial t} - \nabla \phi \)
  

\(\left( \begin{array}{cccc} 0 & {E_x} & {E_y} & {E_z} \\ -{E_x} & 0 & -{B_z} & {B_y} \\ -{E_y} & {B_z} & 0 & -{B_x} \\ -{E_z} & -{B_y} & {B_x} & 0 \end{array} \right)\)

\(=\left( \begin{array}{cccc} 0 & -\frac{\partial {A_x}}{\partial t}-\frac{\partial \phi }{\partial x} & -\frac{\partial {A_y}}{\partial t}-\frac{\partial \phi }{\partial y} & -\frac{\partial {A_z}}{\partial t}-\frac{\partial \phi }{\partial z} \\ \frac{\partial {A_x}}{\partial t}+\frac{\partial \phi }{\partial x} & 0 & \frac{\partial {A_x}}{\partial y}-\frac{\partial {A_y}}{\partial x} & \frac{\partial {A_x}}{\partial z}-\frac{\partial {A_z}}{\partial x} \\ \frac{\partial {A_y}}{\partial t}+\frac{\partial \phi }{\partial y} & \frac{\partial {A_y}}{\partial x}-\frac{\partial {A_x}}{\partial y} & 0 & \frac{\partial {A_y}}{\partial z}-\frac{\partial {A_z}}{\partial y} \\ \frac{\partial {A_z}}{\partial t}+\frac{\partial \phi }{\partial z} & \frac{\partial {A_z}}{\partial x}-\frac{\partial {A_x}}{\partial z} & \frac{\partial {A_z}}{\partial y}-\frac{\partial {A_y}}{\partial z} & 0 \end{array} \right)\)

 

 

 

 

맥스웰 방정식의 표현

• 포텐셜을 통해, 맥스웰 방정식 은 다음과 같이 표현된다
  \(\nabla^2 \varphi + \frac{\partial}{\partial t} \left ( \mathbf \nabla \cdot \mathbf A \right ) = - \frac{\rho}{\varepsilon_0}\)
  \(\left ( \nabla^2 \mathbf A - \frac{1}{c^2} \frac{\partial^2 \mathbf A}{\partial t^2} \right ) - \mathbf \nabla \left ( \mathbf \nabla \cdot \mathbf A + \frac{1}{c^2} \frac{\partial \varphi}{\partial t} \right ) = - \mu_0 \mathbf J\)
  

 

 

역사

 

• http://www.google.com/search?hl=en&tbs=tl:1&q=
• 수학사연표

 

 

메모

 

• Math Overflow http://mathoverflow.net/search?q=

 

 

 

 

수학용어번역

• 단어사전
  
  • http://translate.google.com/#en%7Cko%7C
  • http://ko.wiktionary.org/wiki/
• 발음사전 http://www.forvo.com/search/
• 대한수학회 수학 학술 용어집
  
  • http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=eng_term&fstr=
• 한국통계학회 통계학 용어 온라인 대조표
• 남·북한수학용어비교
• 대한수학회 수학용어한글화 게시판

 

 

매스매티카 파일 및 계산 리소스

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• http://www.wolframalpha.com/input/?i=
• http://functions.wolfram.com/
• NIST Digital Library of Mathematical Functions
• Abramowitz and Stegun Handbook of mathematical functions
• The On-Line Encyclopedia of Integer Sequences
• Numbers, constants and computation
• 매스매티카 파일 목록

 

 

사전 형태의 자료

• http://ko.wikipedia.org/wiki/
• http://en.wikipedia.org/wiki/Electromagnetic_four-potential
• http://en.wikipedia.org/wiki/Mathematical_descriptions_of_the_electromagnetic_field#Potential_field_approach
• The Online Encyclopaedia of Mathematics
• NIST Digital Library of Mathematical Functions
• The World of Mathematical Equations

 

 

 

 

 

관련논문

• http://www.jstor.org/action/doBasicSearch?Query=
• http://www.ams.org/mathscinet
• http://dx.doi.org/

 

 

관련도서

• 도서내검색
  
  • http://books.google.com/books?q=
  • http://book.daum.net/search/contentSearch.do?query=