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

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The discussion revolves around determining the electric potential at the center of a cube with five grounded sides and one insulated side at potential x. It is established that the potential at the center is a linear combination of the potentials from all six sides, based on the principle of superposition. The formula derived is V = (1/6)V', where V' is the potential of the insulated side, and the grounded sides contribute zero potential. This leads to the conclusion that the potential at the center is directly proportional to the potential of the insulated side. The analysis highlights the significance of symmetry and superposition in electrostatics.
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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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