# Superposition in separation method of variables

• Celso

#### 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?

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

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)##?

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.

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 !

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.

Last edited:
• SammyS and BvU