Question

Six point charges are arranged at the vertices of a regular hexagon of side length a (shown in figure) Find the magnitude of electric field at the center of regular hexagon.

• A. $\frac{q}{4\pi {\epsilon }_0{a}^2}$
• B. zero
• C. $\frac{q}{2\pi {\epsilon }_0{a}^2}$
• D. None of these

Answer 1

The correct option is C $\frac{q}{2\pi {\epsilon }_0{a}^2}$

From the given figure

Resultant of $\left[C\right]=2E$

Then,

$\begin{array}{c}{E}_{net}=4E=\frac{4k\theta }{r^2}=\frac{4\theta }{r^2}=\frac{4\theta }{4\pi E_o}=\frac{\theta }{\pi E_o}\end{array}$

Hence, the option $D$ is the correct answer.