Electric field inside an infinte slab of linear density charge of thickness d?

[ENgez]

Homework Statement

An infinite slab of charge with thickness d (from x=0 to x=d) in the x direction has a charge density corrosponding to rho (x) = Ax+B where A and B are positive consants.
Find the electric field at point x1<d

Homework Equations

I know i have to find some guassian surface (a cube i guess) which has the same electric field on both planes which are perpandaculer to the x axis. i tried a few but all were wrong. can anyone point me in the right direction?

The Attempt at a Solution

 

[stevenb]

I know i have to find some guassian surface (a cube i guess) which has the same electric field on both planes which are perpandaculer to the x axis. i tried a few but all were wrong. can anyone point me in the right direction?

Sometimes Coulomb's law is more useful than Gauss' Law, but that is a needlessly complicated method, in this case.

Sometimes you can simplify the approach if you take a result of Coulomb's law or Gauss' Law in a simple case, and use that as a basis to solve a more complicated case. In other words, don't try to apply Coulomb's law or Gauss' Law directly for the full problem, but apply either indirectly, via superposition.

I recommend first deriving (or looking up) the electric field due to an infinitely thin slab of charge, and using superposition to integrate the value of electric field for the full slab of thickness d?

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elesht.html

If you take this approach, be very careful about the direction of the electric field on each side of an infinitely thin sheet.

 

[ENgez]

thanks, i used superposition. problem solved:).