Physics · Electrostatics

JEE Advanced 2022 — Paper 1 — Question 31

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?

Option A:
When $\mathrm{x}=\mathrm{q}$ , the magnitude of the electric field at O is zero.
Correct
Option B:
When $\mathrm{x}=-\mathrm{q}$ , the magnitude of the electric field at O is $\frac{q}{6 \pi \in_{0} a^{2}}$
Correct
Option C:
When $\mathrm{x}=2 \mathrm{q}$ , the potential at O is $\frac{7 q}{4 \sqrt{3} \pi \in_{0} a}$ .
Correct
Option D:
When $x=-3 q$ , the potential at O is $-\frac{3 q}{4 \sqrt{3} \pi \in_{0} a}$

Answer: A, B, C

Step-by-step solution

$\mathbf{A}, \mathbf{B}, \mathbf{C}$ When $\mathrm{x}=\mathrm{q}$ , electric field at O is zero.

When $x=-q$ , electric field at $O$ is, $E=\frac{1}{4 \pi \varepsilon_{0}} \frac{2 q}{(\sqrt{3} a)^{2}}=\frac{q}{6 \pi \varepsilon_{0} a^{2}}$ When $\mathrm{x}=2 \mathrm{q}$ , potential at O is, $V=\frac{7 q}{4 \sqrt{3} \pi \varepsilon_{0} a}$

When $x=-3 q$ , potential at $O$ is, $\mathrm{V}=\frac{2 \mathrm{q}}{4 \sqrt{3} \pi \varepsilon_{0} \mathrm{a}}$

Answer key and solution verified before publishing.

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Exam: JEE Advanced 2022
Paper: Paper 1
Subject: Physics
Chapter: Electrostatics
Topic: Electrostatic Field & motion of charge