Calculating Scalar Potential for a Cube with Point Charges

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SUMMARY

The scalar potential \(\phi\) at the center of the face of a cube with edge length \(a\) and point charges \(q\) at each corner is calculated to be \(\phi = 0.707 \times \frac{q}{\epsilon_0 a}\). This result is derived by considering the contributions from all eight charges and the symmetry of the cube. The angle involved in the calculation is determined using \(\cos(45^\circ) = 0.707\), which is essential for accurately computing the potential at the specified location.

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Midas_Touch
Consider a cube of edge a. There is a point charge q at each corner. Find [tex]\phi[/tex] at the center of the face for which x=a.
The answer to the problem is [tex]\0.707*(q/\epsilon_0*a)[/tex]
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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