Physics
Physics
Problem
Five vertices of a regular hexagon of side carry identical charges , while the sixth vertex carries a charge of the same magnitude. Without detailed calculation, state whether the electric field at the centre of the hexagon is zero or non-zero. If it is non-zero, specify its direction with respect to the hexagon and give a brief justification.Intuitive explanation
The key insight is recognizing that a regular hexagon has six-fold rotational symmetry, but your charge configuration breaks it—five vertices are identical, one is different. Normally, the six identical charges would cancel perfectly at the center by symmetry. However, replacing one with removes one field contribution and reverses another, destroying the cancellation. The net field points away from the vertex with (or equivalently, toward that vertex's opposite side), since you've effectively subtracted twice the field that single charge would have produced.
Intuitive explanation
The key insight is recognizing that a regular hexagon has six-fold rotational symmetry, but your charge configuration breaks it—five vertices are identical, one is different. Normally, the six identical charges would cancel perfectly at the center by symmetry. However, replacing one with removes one field contribution and reverses another, destroying the cancellation. The net field points away from the vertex with (or equivalently, toward that vertex's opposite side), since you've effectively subtracted twice the field that single charge would have produced.