Five positive charges each having charge q are placed at the vertices of a pentagon. Find the electric potential V and electric field E at the center O.

Solution:

Let the distance from center to each vertex be r.

Electric potential due to one charge:

V₁ = kq/r

Total potential:

V = 5kq/r

Electric field vectors due to all five charges cancel each other because of symmetry.

Therefore:

E = 0

Answer:

V = 5kq/r

E = 0