Physics

Physics

Problem

Six point charges are placed at the vertices of a regular hexagon of side 0.10 m0.10\,\text{m} such that the charges alternate in sign around the hexagon: +q+q, −q-q, +q+q, −q-q, +q+q, −q-q where q=3 μCq = 3\,\mu\text{C}. Find the magnitude and direction of the net electrostatic force acting on a +q+q charge placed at the centre of the hexagon.
Intuitive explanation

The key insight is to use symmetry to eliminate most calculations. In a regular hexagon with alternating charges, opposite vertices are equidistant from the center and their charges have opposite signs—so forces from opposite pairs will cancel perfectly. Rather than computing six separate force vectors, identify which pairs cancel by symmetry, then add only the survivors. This transforms a tedious problem into an elegant one.

Intuitive explanation

The key insight is to use symmetry to eliminate most calculations. In a regular hexagon with alternating charges, opposite vertices are equidistant from the center and their charges have opposite signs—so forces from opposite pairs will cancel perfectly. Rather than computing six separate force vectors, identify which pairs cancel by symmetry, then add only the survivors. This transforms a tedious problem into an elegant one.

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