Metallic cube with circular hole

[ShayanJ]

There is a cube with its sides equal to d and its thikness equal to t. It also has a circular hole at its center with radius a (a<<d). Two sides of the cube are maintained at potentials $V_0$ and $-V_0$.
I want to find the potential inside the cube but I see no way for obtaining the boundary conditions: the potential function at the boundary of the hole and the potential of the sides of the cube which are not connected to the battery. I just have no idea.Can anyone help?
Thanks

 

[phyzguy]

This doesn't make any sense to me. Is it a solid cube? If so, the statement that the side = d defines the cube - what then does it mean to say the thickness = t? Is it a hollow cube with side = d and the thickness of the faces = t? If so, how can it have a hole at the center? Do you mean that one or more of the faces has a hole at the center? Also, which two sides have the applied potential? Two opposite sides? Two adjacent sides? Please describe it in more detail or provide a drawing.

 

[ShayanJ]

Sorry...

 

[phyzguy]

That helps. So it is not a cube, unless d = t. Is it a dielectric? Can you use superposition, considering a solid "cube" superposed with a cylinder?

 

[ShayanJ]

That helps. So it is not a cube, unless d = t. Is it a dielectric? Can you use superposition, considering a solid "cube" superposed with a cylinder?

Its a metal, a conductor!
I don't understand. Please clarify a bit!

 

[phyzguy]

OK, so it's a conductor with a current flowing through it. Do you know how to solve the problem without the hole?

 

[ShayanJ]

OK, so it's a conductor with a current flowing through it. Do you know how to solve the problem without the hole?

Yeah, that seems easy.
The potential inside the cuboid is $\phi=Ax+B$ if we take the x-axis to be parallel to its lower edge. The constants A and B can be calculated easily using given potentials for two sides.