Given:
Uniformly distributed Charge on the regular hexagon : q

When a wire is bent in the form of a regular hexagon having charge q uniformly distributed, each point on the hexagon will contribute same magnitude of electric field.
Say, 6 vertices of the hexagon have same charge q.
Thus they will produce same electric field E at the center.
This electric field gets nullified as same magnitude is acting from both sides.
Formula used:
Electric field at a point due to a point charge is given as:
Where k is a constant and k= =9× 10⁹ Nm²C^-2. q is the charge and r is the distance between the point and the charge.
Mathematically:
E₁=E₂
From the figure E₁ is the electric field due to vertex 1 at the center and E₂ is the electric field due to vertex 2 at the center diametrically opposite to vertex 1.
Thus net electric field at center due to 1 and 2 is
E_net = E₁-E₂

∴ E_net = 0

Eventually electric field due to all 6 vertices cancel out each other at the center.
Hence, electric field at the center of the regular hexagon is zero.