JEE Advanced 2026 · Paper 2 · Physics Q8

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PhysicsMultiple correct+4 / -1Question 26 of 54

Consider an electric dipole comprising two charges $+q$ and $-q$ each with mass $m$ , separated by a fixed distance $d$ and initially at rest with its dipole moment pointing along $\hat\imath$ . A uniform electric field $E\hat\jmath$ is turned on at time $t=0$ and it is turned off at $t=t_f$ , when the dipole moment makes an angle $\theta_f$ with $\hat\imath$ . Neglecting any sources of energy loss, correct option(s) is/are:

The center of mass of the dipole is deflected towards

\hat\jmath

in the presence of the field.

If the magnitude of the final angular velocity

\omega_f=\sqrt{\dfrac{2qE}{md}}

, then

\theta_f=\dfrac\pi6

\theta_f=\pi/3

, then the change in kinetic energy of the dipole is given by

2\sqrt3\,qEd

For

\theta_f=\pi/4

, the dipole rotates around its center of mass with a constant angular velocity after

t>t_f

Answer and worked solution

Official answer: B, D

Translation. The forces $\pm qE\hat\jmath$ cancel, so the centre of mass stays at rest. (A) false.

Rotation. Let $\theta$ be the angle of $\vec p$ from $\hat\imath$ . Then $U=-pE\sin\theta$ and $I=2m\left(\frac d2\right)^2=\frac{md^2}2$ . Starting from rest at $\theta=0$ ,
$\tfrac12I\omega^2=qEd\sin\theta\implies\omega^2=\frac{4qE\sin\theta}{md}.$

(B) $\omega_f^2=\dfrac{2qE}{md}$ gives $\sin\theta_f=\frac12$ , so $\theta_f=\frac\pi6$ . (The dipole swings between 0 and $\pi$ , so $\frac{5\pi}6$ gives the same $\omega_f$ ; that is why the key also accepts D alone.)
(C) $\Delta K=qEd\sin\frac\pi3=\frac{\sqrt3}2qEd$ , not $2\sqrt3\,qEd$ . False.
(D) After $t_f$ there is no force or torque. At $\theta_f=\frac\pi4$ , $\omega_f\ne0$ , so the dipole spins about its centre of mass at constant angular velocity. True.

Topics:Electric dipole Rotational kinetic energy

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