Six charges each +3q are placed at the corners of a regular hexagon of each side 'a'. The electric field at the center of the hexagon is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Zero
The field at the centre is the vector sum of the fields of the six charges, and symmetry decides it. The centre of a regular hexagon is at the same distance a from every corner, so each charge produces a field of the same magnitude
\( \displaystyle E_1 = \frac{1}{4\pi\varepsilon_0}\frac{3q}{a^{2}} \)
directed away from that corner (the charges are positive). Opposite corners lie on a line through the centre, so their fields are equal in magnitude and opposite in direction and cancel in pairs. The six charges form three such pairs, so
\( \vec{E}_{\mathrm{net}} = \vec{0} \)