MandysNotes

Saturday, 08 February 2014 19:51

Maxwell's Equations

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Gauss's Law:

 

\[ \nabla \cdot {\color{WildStrawberry} E} = {\color{RedOrange}4\pi} {\color{ForestGreen} \rho} \]

 

Ampere's Law:


\[ \nabla \mathbf{\times} {\color{RoyalBlue} B } = \frac{{\color{RedOrange}4\pi}}{{\color{Goldenrod}c}} {\color{Purple} J } + \frac{1}{{\color{Goldenrod}c}} \frac{\partial {\color{WildStrawberry} E }}{ \partial t} \]

 

GaussianIntegral

 

 

Suppose we are given a certain quantity of an ideal gas at some fixed temperature, and we want to know what sort of distribution of velocities to associate with this gas.
That is, given a range of velocities, \[\Delta v = v_\beta - v_\alpha, \]
what is the number of molecules, \[\Delta n,  \]with velocities in the region of phase space \[\Delta v= \Delta v_x \Delta v_y \Delta v_z? \]

NOTRad