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 \(\frac{q}{6\pi∈_ 0 a^2}\)

(C) When x = 2q, the potential at O is \(\frac{7q}{4\sqrt{3}\pi ∈_ 0 a}\)

(D) When x = − 3q , the potential at O is \(\frac{3q}{4\sqrt{3}\pi ∈_0 a}\)

Answer 1

(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 \(\frac{q}{6\pi∈_ 0 a^2}\)

(C) When x = 2q, the potential at O is \(\frac{7q}{4\sqrt{3}\pi ∈_ 0 a}\)

When x = q, electric field at O is zero. 

When x = –q, electric field at O is,