Question

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.

Answer 1

We know that the length of diagonal of the cube side b is `sqrt(3b^(2)) = b sqrt(3)`
`:.` Distance between center of cube and each vertex, `r = (b sqrt(3))/(2)`
AS `V = (1)/(4pi in_(0)) (q)/(r )`
and 8 charges each of value q are present at the eight verticies of the cube, therefore,
`V = (1)/(4pi in_(0)) (8q)/(b sqrt(3)//2) or V = (4q)/(sqrt(3) pi in_(0) b)`
Further electric field intensity at the center due to all the eight charges is zero, because the fileds due to individual charges cancel in pairs.