Electric Field in a tiny cubical cavity within three piled disks of charge.

[ELESSAR TELKONT]

Homework Statement

A charge distribution has the shape of a very large disk of thickness $$3d$$. This disk has three layers of uniform densities $$\rho_{1},\rho_{2},\rho_{3}$$ and thickness $$d$$ each one. Within the layer with density $$\rho_{2}$$ exists a tiny cubical cavity in such a manner that two of its faces are parallel to the interfaces between layers. Find the electrostatic field at the center of the cubical cavity.

Homework Equations

The Attempt at a Solution

I have tried to solve it basically in two manners. Directly calculating the potential due to the disk layers and using the fact that
$$\varphi(x)=\frac{1}{4\pi\epsilon_{0}}\int_{V}\frac{\rho}{\left\vert r-r'\right\vert}dV'+\frac{1}{4\pi}\int_{S}\left [ -\phi \frac{r-r'}{\left\vert r-r'\right\vert^{3}}+\frac{\nabla '\phi}{\left\vert r-r'\right\vert}\right ]\cdot n' dS'$$. My problem in both strategies is that how can I calculate the potential due to the layer where the cubical cavity is and in the second form is how to calculate the normal derivative of potential.

Is there any technic to do this problem easier?

 

[gabbagabbahey]

Why not just use the superposition principle?

 

[ELESSAR TELKONT]

How, give me a hint

 

[gabbagabbahey]

What happens if you superimpose a cube of charge density $-\rho_2$ onto a solid 3 layered disk (like the one you describe in your problem statement, but without the cavity)?