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Metallic cube with circular hole

  1. Apr 23, 2014 #1

    ShayanJ

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    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 [itex] V_0 [/itex] and [itex] -V_0 [/itex].
    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
     
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  3. Apr 23, 2014 #2

    phyzguy

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    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.
     
  4. Apr 24, 2014 #3

    ShayanJ

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    Sorry...
     

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  5. Apr 24, 2014 #4

    phyzguy

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    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?
     
  6. Apr 24, 2014 #5

    ShayanJ

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    Its a metal, a conductor!
    I don't understand. Please clarify a bit!
     
  7. Apr 24, 2014 #6

    phyzguy

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    OK, so it's a conductor with a current flowing through it. Do you know how to solve the problem without the hole?
     
  8. Apr 24, 2014 #7

    ShayanJ

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    Yeah, that seems easy.
    The potential inside the cuboid is [itex] \phi=Ax+B [/itex] 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.
     
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