Potential Inside Cube: What Is the Center's Potential?

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SUMMARY

The potential at the center of a cube with five grounded sides and one insulated side at potential V' is calculated using the principle of superposition. The potential V at the center is determined to be V = 1/6 V', where V' is the potential of the insulated side. This conclusion arises from the linear combination of the potentials of all six sides, with the grounded sides contributing zero potential. The constant c is established as 1/6, confirming the relationship between the center's potential and the insulated side's potential.

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EFuzzy
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A cube has 5 sides grounded, and an insulated sixth side at potential x. What is the potential at the center of the cube?

The solution states that the potential at the center must be a linear combination of the potentials of the six sides. Why is that?

Thanks,
EFuzzy
 
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I guess using principle of superposition...
V=c(v1+v2+...+v6)for each side, where c is a constant . assuming they have the same potential... V=c6V so c=1/6
now v1=0=v2=...=v5 and v6=V'
so V=1/6(0+0+..+0+V')=1/6V'
 

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