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 at the center of the cube.

Answer 1

Let r = distance of each charge at vertex from the center of cube.

Potential at the centre O = Potential due to each of 8 charges

= \(\frac{1}{4\piɛ_o}. \frac{8q}{r}\)

∴ Potential at O, V = \(\frac{1}{4\piɛ_o}\ \times\ \frac{8q\times2}{\sqrt3b}\)

= \(\frac{4q}{\sqrt3\piɛ_ob}\)

However, electric field inside a symmetrically shaped surface is zero since fields will mutually cancel each other.