A wire is shaped into a regular hexagon, and a total charge q is uniformly distributed along it. Determine the electric field at the centre. You can answer this without performing any numerical calculations.

Step-by-step solution

A regular hexagon is a highly symmetric geometric figure. Since the charge q is uniformly distributed along the wire, each of the six sides of the hexagon has the same linear charge density and produces an electric field of equal magnitude at the centre. For every side of the hexagon, there is an identical side directly opposite to it. The electric field vectors produced by any pair of opposite sides at the centre are equal in magnitude but opposite in direction. Thus, the electric fields from all pairs of opposite