Finding electric field for non-uniform charge distribution ρ = ρ₀x/a using Gauss' law

[magnifik]

What is the electric field for the following charge distribution:

ρ = ρ₀ x/a for -a < x < a
0 elsewhere

Use the differential form of Gauss' Law.

I know that the differential form is $\nabla$ . D = ρ_v and that E = D/ε, but how do I find D from what is given? Do i integrate the charge distribution with respect to x?

 

[susskind_leon]

Nop, you integrate over the electric field that is associated with the charge density.
http://en.wikipedia.org/wiki/Electrostatics#The_electric_field
So you need to perform the integral over p(r) (r-r_0)/(|r-r_0|^3)

 

[magnifik]

Nop, you integrate over the electric field that is associated with the charge density.
http://en.wikipedia.org/wiki/Electrostatics#The_electric_field
So you need to perform the integral over p(r) (r-r_0)/(|r-r_0|^3)

how would i do a triple integral with what I'm given?

 

[susskind_leon]

http://emtmadeeasy.blogspot.com/2010/01/electric-field-intensity-due-to-finite.html
http://www.ece.ksu.edu/~khc/notes/emt/finite-line-field.pdf
Hope that helps