A cube of side b has a charge q at each of its vertices. Determine the potential and electric field due to this charge array at the center of the cube.

Explanation

To solve the problem of determining the electric potential and electric field at the center of a cube with a charge \( q \) at each vertex, we can follow these steps:

### Step 1: Determine the distance from the center to a vertex
The center of the cube is equidistant from all vertices. The distance from the center of the cube to any vertex can be calculated using the formula for the diagonal of a cube. The diagonal length \( d \) of the cube can be given by:

\[ d = \sqrt{3}b \]
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