Electrostatic – A regular hexagon has charges placed at all six vertices

Alternate vertices carry charges +q and −q.

Find the magnitude and direction of the electric field at the center of the hexagon.

Given:

A regular hexagon has charges at all six vertices.

Alternate vertices carry +q and −q.

Distance from center to each vertex = a.

Electric field due to one charge at center:

Now consider one opposite pair (+q,−q).

The field due to +q is away from the charge while the field due to −q is towards the charge.

Hence both fields act in the same direction.

There are three such equal field vectors corresponding to the three opposite pairs.

These three vectors are separated by 120°.

The resultant of three equal vectors separated by 120° is zero.