Understanding Poisson's Equation: General Forms

[OllyRutts]

I am having trouble determining what the general form of Poisson's equation would be between

and

Can they both be called the general form?

 

[BvU]

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.

 

[OllyRutts]

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 textbook I am using is using for gauss's law in terms of D=\varepsilon\varepsilon_0E

So any is appropriate for the general form?

 

[BvU]

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.

 

[OllyRutts]

Thanks much appreciated.