An electric dipole of mass m , charge q , and length l is placed in a uniform electric field overrightarrow E = E 0 hat i . When the dipole is rotated slightly from its equilibrium position and released, the time period of its oscillations will be :

Physics · Electrostatics

JEE Main 2025 — 29 January, Morning Shift — Question 25

An electric dipole of mass $m$ , charge $q$ , and length $l$ is placed in a uniform electric field $\overrightarrow{\mathrm{E}}=\mathrm{E}_{0} \hat{\mathrm{i}}$ . When the dipole is rotated slightly from its equilibrium position and released, the time period of its oscillations will be :

Option A:
$\frac{1}{2 \pi} \sqrt{\frac{2 \mathrm{~m} l}{\mathrm{qE}_{0}}}$
Option B:
$2 \pi \sqrt{\frac{\mathrm{~m} l}{\mathrm{qE}_{0}}}$
Option C:
$\frac{1}{2 \pi} \sqrt{\frac{\mathrm{~m} l}{2 \mathrm{qE}_{0}}}$
Option D:
$2 \pi \sqrt{\frac{m l}{2 q E_{0}}}$
Correct

Answer: D

Step-by-step solution

$\mathrm{I} \omega 2 \theta=\mathrm{q} \ell \mathrm{E}_{0} \theta$

$2 \mathrm{~m}\left(\frac{\ell}{2}\right)^{2} \omega^{2}=\mathrm{q} \ell \mathrm{E}_{0}$

$\omega^{2}=\frac{2 \mathrm{qE}_{0}}{\mathrm{~m} \ell}$

$\mathrm{T}=2 \pi \sqrt{\frac{\mathrm{~m} \ell}{2 \mathrm{qE}_{0}}}$

Answer key and solution verified before publishing.

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Exam: JEE Main 2025
Paper: 29 January, Morning Shift
Subject: Physics
Chapter: Electrostatics
Topic: Electric Dipole

Match List-I with List-II. List-I List-II --- --- --- --- (A) Electric field inside (distance r 0 from center) of a uniformly charged…

Answer: D

Step-by-step solution

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