Question

Six charges are placed around a regular hexagon of side length a as shown in the figure Five of them have charge $q$, and the remaining one has charge $x$ The perpendicular from each charge to the nearest hexagon side passes through the center $O$ of the hexagon and is bisected by the side Which of the following statement(s) is(are) correct in SI units?

• A. When $x=q$, the magnitude of the electric field at $O$ is zero.
• B. When $x=-q$, the magnitude of the electric field at $O$ is $\frac{q}{6 \pi \in_0 a^2}$.
• C. When $x=2 q$, the potential at $O$ is $\frac{7 q}{4 \sqrt{3} \pi \in_0 a}$.
• D. When $x=-3 q$, the potential at $O$ is $\frac{3 q}{4 \sqrt{3} \pi \epsilon_0 a}$.

Answer 1

Answer: (A), (B), (C)

When $x=q$, the magnitude of the electric field at $O$ is zero.

Answer 2

When $x=q$, the magnitude of the electric field at $O$ is zero.
When $x=-q$, the magnitude of the electric field at $O$ is $\frac{q}{6 \pi \in_0 a^2}$.
When $x=2 q$, the potential at $O$ is $\frac{7 q}{4 \sqrt{3} \pi \in_0 a}$.