Question

Four equal charges of value $+$Q are placed at any four vertices of a regular hexagon of side 'a'. By suitable choosing the vertices, what can be the maximum possible magnitude of electric field at the centre of the hexagon?

• A. $\frac{Q}{4\pi {\epsilon }_0{a}^2}$
• B. $\frac{\sqrt{2}Q}{4\pi {\epsilon }_0{a}^2}$
• C. $\frac{\sqrt{3}Q}{4\pi {\epsilon }_0{a}^2}$
• D. $\frac{2Q}{4\pi {\epsilon }_0{a}^2}$

Answer 1

Answer: (C)

$\frac{\sqrt{3}Q}{4\pi {\epsilon }_0{a}^2}$

\To maximize the electric field at the centre both -q should be present at adjacent vertices $E=\sqrt{E_1^2+E_1^2+E_1^2}=\sqrt{3}{E}_1$
$E_1=\frac{kQ}{a^2}=\frac{Q}{4\pi {\epsilon }_0{a}^2}$
$E=\frac{\sqrt{3}Q}{4\pi {\epsilon }_0{a}^2}$.