Calculating Scalar Potential for a Cube with Point Charges

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To calculate the scalar potential at the center of a face of a cube with point charges at each corner, consider the contributions from all eight charges. The potential at that point is determined by the scalar potential equation, factoring in the distances and angles to each charge. Specifically, the angle involved is 45 degrees, leading to a cosine value of approximately 0.707. The final expression for the potential at the specified location is 0.707*(q/ε₀*a). Understanding the symmetry of the cube and the varying distances from the charges is crucial for solving the problem.
Midas_Touch
Consider a cube of edge a. There is a point charge q at each corner. Find \phi at the center of the face for which x=a.
The answer to the problem is \0.707*(q/\epsilon_0*a)
I have to use the the scalar potential equation, but I have been stuck on this problem for a while. I know that I have to consider the angle which is cos45 = 0.707. I am not sure I understand what they are asking in the problem.
 
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Consider the symmetry of the cube, and remember that the potential is the sum of the potential of each charge. There are 8 charges.
 
the "1 spot" on a dice cube ...
each charge contributes its own portion to the potential there,
since it is not the same distance from each source.
 

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