184_notes:maxwells_eq

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
184_notes:maxwells_eq [2017/11/30 22:30] – [The Four Maxwell's Equations] dmcpadden184_notes:maxwells_eq [2021/07/06 17:53] (current) – bartonmo
Line 1: Line 1:
 Section 22.4 and 23.1 in Matter and Interactions (4th edition) Section 22.4 and 23.1 in Matter and Interactions (4th edition)
 +
 +/*[[184_notes:symmetry|Previous Page: Symmetry and Mathematical Tools]]*/
  
 ===== Putting Together Maxwell's Equations ===== ===== Putting Together Maxwell's Equations =====
Line 6: Line 8:
 {{youtube>pKJvn57geS4?large}}  {{youtube>pKJvn57geS4?large}} 
  
-==== The Four Maxwell's Equations ====+===== The Four Maxwell's Equations =====
 First we have [[184_notes:gauss_ex|Gauss's Law]], which says that **charges make electric fields**: First we have [[184_notes:gauss_ex|Gauss's Law]], which says that **charges make electric fields**:
 $$\int \vec{E} \bullet d\vec{A} = \frac{Q_{enc}}{\epsilon_0}$$ $$\int \vec{E} \bullet d\vec{A} = \frac{Q_{enc}}{\epsilon_0}$$
Line 24: Line 26:
 These equations are important because, as we learned, once you have the [[184_notes:pc_efield|electric]] or [[184_notes:moving_q|magnetic field]], you can relate those fields to the [[184_notes:pc_force|electric]] or [[184_notes:q_b_force|magnetic force]]; to [[184_notes:pc_energy|energy]], [[184_notes:pc_potential|electric potential]], or work; and apply those principles to circuit applications like [[184_notes:cap_in_cir|capacitors]], [[184_notes:r_energy|resistors]], and [[184_notes:current|current]]. Ultimately, with the [[184_notes:charge|conservation of charge]], these Maxwell's equations govern how charged particles behave and interact.  These equations are important because, as we learned, once you have the [[184_notes:pc_efield|electric]] or [[184_notes:moving_q|magnetic field]], you can relate those fields to the [[184_notes:pc_force|electric]] or [[184_notes:q_b_force|magnetic force]]; to [[184_notes:pc_energy|energy]], [[184_notes:pc_potential|electric potential]], or work; and apply those principles to circuit applications like [[184_notes:cap_in_cir|capacitors]], [[184_notes:r_energy|resistors]], and [[184_notes:current|current]]. Ultimately, with the [[184_notes:charge|conservation of charge]], these Maxwell's equations govern how charged particles behave and interact. 
  
-==== Limitations on Classical E&M ====+===== Limitations on Classical E&M =====
  
 This theory of electromagnetism is classical in that it applies to systems of many atoms and electrons. We have constructed arguments for single charges or even small atomic systems, but in reality, these charges and systems are governed by quantum mechanics. So, while we might have a classical picture of the atom and electron cloud, a better model is more complicated and requires a quantum theory of electromagnetism in which both atomic systems and the field are treated quantum mechanically. (These topics are typically introduced in a modern physics course.) This reformulation of electromagnetism helps us do cutting research and development as electronic systems become increasingly smaller and push on the limits of quantum mechanics. This theory of electromagnetism is classical in that it applies to systems of many atoms and electrons. We have constructed arguments for single charges or even small atomic systems, but in reality, these charges and systems are governed by quantum mechanics. So, while we might have a classical picture of the atom and electron cloud, a better model is more complicated and requires a quantum theory of electromagnetism in which both atomic systems and the field are treated quantum mechanically. (These topics are typically introduced in a modern physics course.) This reformulation of electromagnetism helps us do cutting research and development as electronic systems become increasingly smaller and push on the limits of quantum mechanics.
  
 Even so, this classical theory is one of the most complete theories in science for the range of physical systems it can describe. It works at the astronomical scale and is consistent with relativity, and it works down to the microscopic level (up to the quantum limit).  It is truly an incredible theory. Even so, this classical theory is one of the most complete theories in science for the range of physical systems it can describe. It works at the astronomical scale and is consistent with relativity, and it works down to the microscopic level (up to the quantum limit).  It is truly an incredible theory.
  • 184_notes/maxwells_eq.1512081052.txt.gz
  • Last modified: 2017/11/30 22:30
  • by dmcpadden