"Electromagnetics"의 두 판 사이의 차이
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imported>Pythagoras0 |
imported>Pythagoras0 |
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==gauge invariance== | ==gauge invariance== | ||
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* the electromagnetic potential is a connection on a U(1)-bundle on spacetime whose curvature is the electromagnetic field | * the electromagnetic potential is a connection on a U(1)-bundle on spacetime whose curvature is the electromagnetic field | ||
* the electromagnetism is a gauge field theory with structure group U(1) | * the electromagnetism is a gauge field theory with structure group U(1) | ||
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==Lorentz force== | ==Lorentz force== | ||
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* almost all forces in mechanics are conservative forces, those that are functions only of positions, and certainly not functions of velocities | * almost all forces in mechanics are conservative forces, those that are functions only of positions, and certainly not functions of velocities | ||
* Lorentz force is a rare example of velocity dependent force | * Lorentz force is a rare example of velocity dependent force | ||
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==polarization of light== | ==polarization of light== | ||
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* has two possibilites | * has two possibilites | ||
** what does this mean? | ** what does this mean? | ||
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==Lagrangian formulation== | ==Lagrangian formulation== | ||
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==Hamiltonian formulation== | ==Hamiltonian formulation== | ||
| − | + | * total energy of a charge particle in an electromagnetic field | |
| − | * total energy of a charge particle in an electromagnetic field<math>E=\frac{1}{2m}(p_j-eA_{j})(p_j-eA_j)+q\phi</math> | + | :<math>E=\frac{1}{2m}(p_j-eA_{j})(p_j-eA_j)+q\phi</math> |
* replace the momentum with the canonical momentum | * replace the momentum with the canonical momentum | ||
** similar to covariant derivative | ** similar to covariant derivative | ||
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==force on a particle== | ==force on a particle== | ||
| + | * force on a particle is same as | ||
| + | :<math>e\mathbf{E}+e\mathbf{v}\times \mathbf{B}</math> | ||
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==메모== | ==메모== | ||
| 73번째 줄: | 55번째 줄: | ||
* Feynman's proof of Maxwell equations and Yang's unification of electromagnetic and gravitational Aharonov–Bohm effects | * Feynman's proof of Maxwell equations and Yang's unification of electromagnetic and gravitational Aharonov–Bohm effects | ||
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==related items== | ==related items== | ||
2014년 1월 29일 (수) 01:40 판
basic history
- Leyden jar : capacitor
- Volta vs Galvani
- Humphrey Davy
- Oesrsted
- Faraday
- Maxwell
- Lodge
- Marconi
- Tesla : alternating current
gauge invariance
- the electromagnetic potential is a connection on a U(1)-bundle on spacetime whose curvature is the electromagnetic field
- the electromagnetism is a gauge field theory with structure group U(1)
Lorentz force
- almost all forces in mechanics are conservative forces, those that are functions only of positions, and certainly not functions of velocities
- Lorentz force is a rare example of velocity dependent force
polarization of light
- has two possibilites
- what does this mean?
Lagrangian formulation
Hamiltonian formulation
- total energy of a charge particle in an electromagnetic field
\[E=\frac{1}{2m}(p_j-eA_{j})(p_j-eA_j)+q\phi\]
- replace the momentum with the canonical momentum
- similar to covariant derivative
force on a particle
- force on a particle is same as
\[e\mathbf{E}+e\mathbf{v}\times \mathbf{B}\]
메모
- http://www.math.toronto.edu/~colliand/426_03/Papers03/C_Quigley.pdf
- Feynman's proof of Maxwell equations and Yang's unification of electromagnetic and gravitational Aharonov–Bohm effects
encyclopedia
- http://ko.wikipedia.org/wiki/
- http://en.wikipedia.org/wiki/Classical_electromagnetism
- http://en.wikipedia.org/wiki/Maxwell's_equations
- http://en.wikipedia.org/wiki/Maxwell's_equations#Differential_geometric_formulations
- http://en.wikipedia.org/wiki/Covariant_formulation_of_classical_electromagnetism
- http://en.wikipedia.org/wiki/electrical_current
- http://en.wikipedia.org/wiki/Four-current
books
- ELECTROMAGNETIC THEORY AND COMPUTATION
- The Early History of Radio from Faraday to Marconi