Poisson's Equation

  • Thread starter OllyRutts
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  • #1
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I am having trouble determining what the general form of Poisson's equation would be between

upload_2017-11-22_13-10-41.png

and

upload_2017-11-22_13-12-50.png


Can they both be called the general form?
 

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Answers and Replies

  • #2
BvU
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The 'general form' has not been trademarked or anything. One could equally well claim that ##\ \Delta\phi = f \ ## is the general form.

I do wonder where you got this form from: I find ##\varepsilon\varepsilon_0## very ugly (I am used to ## \varepsilon=\varepsilon_r\varepsilon_0## ) and I don't know where the ##f## in your first expression comes from.
 
  • #3
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The 'general form' has not been trademarked or anything. One could equally well claim that ##\ \Delta\phi = f \ ## is the general form.

I do wonder where you got this form from: I find ##\varepsilon\varepsilon_0## very ugly (I am used to ## \varepsilon=\varepsilon_r\varepsilon_0## ) and I don't know where the ##f## in your first expression comes from.

I should have said this relates to a LIH dielectric material
pf is the free charge density
I guess the text book im using is using for gauss's law in terms of D=\varepsilon\varepsilon_0E

So any is appropriate for the general form?
 
  • #4
BvU
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I should say so, yes.

tip: use ## [ ...##\TeX ## code ] ## as ##\LaTeX## delimiters to get ##{\bf D} =\varepsilon\varepsilon_0 {\bf E} ##

and use subscripts to distinguish factors from, well, subscripts.
 
  • #5
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Thanks much appreciated.
 

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