User Tools

Site Tools


models:classical_electrodynamics

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revision Previous revision
Next revision
Previous revision
models:classical_electrodynamics [2018/05/05 11:52]
jakobadmin ↷ Links adapted because of a move operation
models:classical_electrodynamics [2019/07/01 09:20] (current)
129.13.36.189 [Research]
Line 5: Line 5:
 <tabbox Intuitive> ​ <tabbox Intuitive> ​
  
 +
 +It is a model in the framework of [[theories:​classical_field_theory|classical field theory]]. ​
  
 <​blockquote>​Fields in physics are something which associate with each point in space and with each instance in time a quantity. In case of electromagnetism this is a quantity describing the electric and magnetic properties at this point. Each of these two properties turn out to have a strength and a direction. Thus the electric and magnetic fields associate with each point in space and time an electric and a magnetic magnitude and a direction. For a magnetic field this is well known from daily experience. Go around with a compass. As you move, the magnetic needle will arrange itself in response to the geomagnetic field. Thus, this demonstrates that there is a direction involved with magnetism. That there is also a strength involved you can see when moving two magnets closer and closer together. How much they pull at each other depends on where they are relative to each other. Thus there is also a magnitude associated with each point. The same actually applies to electric fields, but this is not as directly testable with common elements. Ok, so it is now clear that electric and magnetic fields have a direction and a magnitude. Thus, at each point in space and time six numbers are needed to describe them: two magnitudes and two angles each to determine a direction. <​blockquote>​Fields in physics are something which associate with each point in space and with each instance in time a quantity. In case of electromagnetism this is a quantity describing the electric and magnetic properties at this point. Each of these two properties turn out to have a strength and a direction. Thus the electric and magnetic fields associate with each point in space and time an electric and a magnetic magnitude and a direction. For a magnetic field this is well known from daily experience. Go around with a compass. As you move, the magnetic needle will arrange itself in response to the geomagnetic field. Thus, this demonstrates that there is a direction involved with magnetism. That there is also a strength involved you can see when moving two magnets closer and closer together. How much they pull at each other depends on where they are relative to each other. Thus there is also a magnitude associated with each point. The same actually applies to electric fields, but this is not as directly testable with common elements. Ok, so it is now clear that electric and magnetic fields have a direction and a magnitude. Thus, at each point in space and time six numbers are needed to describe them: two magnitudes and two angles each to determine a direction.
Line 21: Line 23:
  
  
-Classical electrodynamics describes the interplay of light and charged objects via the [[equations:​maxwell_equations|Maxwell equations]] and additionally the [[equations:​lorentz_force_law]],​ +Classical electrodynamics describes the interplay of light and charged objects via the [[equations:​maxwell_equations|Maxwell equations]] ​(the static limit is known as [[formulas:​coulombs_law|Coulomb force law]]) ​and additionally the [[formulas:​lorentz_force_law]],​
  
 +----
  
 **Recommended Textbooks: **Recommended Textbooks:
 ** **
  
-  * Feynman Lectures Vol. 2+  * [[http://​www.feynmanlectures.caltech.edu/​II_toc.html|Feynman Lectures Vol. 2]]
   * A student'​s guide to Maxwell'​s equations by  Daniel A. Fleisch   * A student'​s guide to Maxwell'​s equations by  Daniel A. Fleisch
  
Line 41: Line 43:
 It is possible to formulate electrodynamics in a completely coordinate-free way with the help of [[advanced_tools:​differential_forms]]. ​ It is possible to formulate electrodynamics in a completely coordinate-free way with the help of [[advanced_tools:​differential_forms]]. ​
  
-This is described perfectly in “Geometrical methods of mathematical physics” by Schutz starting at page 175. Alternatively a great discussion of this modern approach to classical electrodynamics can be found in [[books:​baez_muniain|Gauge Field Knots and Gravity]] by John Baez and Javier P Muniain+This is described perfectly in “Geometrical methods of mathematical physics” by Schutz starting at page 175. Alternatively a great discussion of this modern approach to classical electrodynamics can be found in [[resources:books:​baez_muniain|Gauge Field Knots and Gravity]] by John Baez and Javier P Muniain
    
 An important aspect of this modern perspective is how the homogeneous Maxwell equations follow directly as generalized [[advanced_tools:​bianchi_identities|Bianchi identities]],​ if we invoke [[theorems:​noethers_theorems|Noether'​s second theorem]] from the invariance of the action under the electromagnetic [[advanced_tools:​gauge_symmetry|gauge group]]. ​ An important aspect of this modern perspective is how the homogeneous Maxwell equations follow directly as generalized [[advanced_tools:​bianchi_identities|Bianchi identities]],​ if we invoke [[theorems:​noethers_theorems|Noether'​s second theorem]] from the invariance of the action under the electromagnetic [[advanced_tools:​gauge_symmetry|gauge group]]. ​
Line 56: Line 58:
 It describes electric and magnetic fields, and as a consequence also X-rays, and every other form of electromagnetic wave. It describes electric and magnetic fields, and as a consequence also X-rays, and every other form of electromagnetic wave.
  
-In addition, electrodynamics explains how electrodynamics and magnetism are related. It has now been superseded by [[theories:​quantum_field_theory|Quantum Electrodynamics]]. However, classical electrodynamics is still an important approximation for many engineering applications. ​+In addition, electrodynamics explains how electrodynamics and magnetism are related. It has now been superseded by [[theories:​quantum_field_theory:canonical|Quantum Electrodynamics]]. However, classical electrodynamics is still an important approximation for many engineering applications. ​
  
 For example, classical electrodynamics is crucial for radio transmissions. ​ For example, classical electrodynamics is crucial for radio transmissions. ​
Line 69: Line 71:
 This is known as premetric approach and is described in detail in the book  "​Foundations of Classical Electrodynamics:​ Charge, Flux, and Metric"​ by F. W. Hehl and Yu. N. Obukhov. ​ This is known as premetric approach and is described in detail in the book  "​Foundations of Classical Electrodynamics:​ Charge, Flux, and Metric"​ by F. W. Hehl and Yu. N. Obukhov. ​
  
-In addition, the electrodynamics and especially the Maxwell equations are modified if [[models:​speculative_models:​axion|axions]] exist. This is known as [[https://​inspirehep.net/​record/​1337434/​files/​26-Kuriksha.pdf|axion electrodynamics]] and was first noted in  F. Wilczek, Phys. Rev. Lett. 58, 1799 (1987).+In addition, the electrodynamics and especially the Maxwell equations are modified if [[models:​speculative_models:​axion|axions]] exist. This is known as [[https://​inspirehep.net/​record/​1337434/​files/​26-Kuriksha.pdf|axion electrodynamics]] and was first noted in  F. Wilczek, Phys. Rev. Lett. 58, 1799 (1987). The main idea here is that if the theta parameter can change in space and time $\theta=\theta(x,​t)$,​ the term $\theta F \tilde F$ directly influences the equations of motion. This is discussed explicitly in Section 1.2 "The Theta Term" in [[http://​www.damtp.cam.ac.uk/​user/​tong/​gaugetheory/​gt.pdf|Tong'​s lectures on gauge theory]].
  
 The Maxwell equations in the presence of axions read The Maxwell equations in the presence of axions read
models/classical_electrodynamics.1525513968.txt.gz · Last modified: 2018/05/05 09:52 (external edit)