Superposition in separation method of variables

[Celso]

Homework Statement

In a cube, the specified boundary counditions are V = $V_{0}$ in the $z = 0$ and $z = d$ planes and $V = 0$ for the other sides. Knowing the solution for when only one of the z planes is kept at $V = V_{0}$ how is it possible to use superposition to know $V(r)$ in this situation?

Relevant Equations

$\nabla^2 V = 0$

Each different boundary condition means a different charge configuration, how can this problem be solved using superposition?

 

[BvU]

Seems very unlikely to me. Anyone says it can be ?

 

[kuruman]

Let $\Phi_0(x,y,z)$ = solution when only the face at z = 0 is at $V_0$.
Let $\Phi_d(x,y,z)$ = solution when only the face at z = d is at $V_0$.
Assuming that the side of the cube is $d$, isn't it true that $\Phi_d(x,y,z)=\Phi_0(x,y,d-z)$?

 

[hutchphd]

Can you create a square pulse using two step functions? That is the crux of the question. I won't give the answer, as it is homework.

 

[BvU]

Seems very unlikely to me. Anyone says it can be ?

Ah! I get it: the exercise text as it was given to you says so . Then it is most likely true, hmm ?
And @kuruman is giving you (much) more than just a hint !

 

[kuruman]

Ah! I get it: the exercise text as it was given to you says so . Then it is most likely true, hmm ?
And @kuruman is giving you (much) more than just a hint !

It's easy to assume that the problem is asking for the solution. Perhaps I was overly generous when I posted but I wanted to point OP in the right direction and there is still quite a bit to be said to complete a formal answer.