JEE Main · 2020 · 06 Sep 2020 · Shift 2 · Electrostatics

Two identical electric point dipoles have dipole moments

p_{1} = p \hat{i}

and

p_{2} = - p \hat{i}

and are held on the

x

axis at distance '

a

' from each other. When released, they move along the

x

-axis with the direction of their dipole moments remaining unchanged. If the mass of each dipole is '

m

', their speed when they are infinitely far apart is:

(A) $\frac{p}{a} \frac{1}{π ϵ _{0} ma}$
(B) $\frac{p}{a} \frac{1}{2 π ϵ _{0} ma}$ ✓ Correct
(C) $\frac{p}{a} \frac{2}{π ϵ _{0} ma}$
(D) $\frac{p}{a} \frac{3}{2 π ϵ _{0} ma}$

Answer: (B)

Solution

Treat this with energy conservation. The two dipoles point in opposite directions along the line joining them, so their mutual axial interaction energy is

U_{i} = \frac{1}{4 π ϵ _{0}} \frac{2 p ^{2}}{a ^{3}}

, and this is the only store of energy when they are released from rest. By the time they are infinitely far apart the interaction energy is zero and that energy has gone entirely into kinetic energy, shared equally by the two equal masses:

\frac{1}{4 π ϵ _{0}} \frac{2 p ^{2}}{a ^{3}} = 2 \times \frac{1}{2} m v^{2}

. Solving for the common speed,

v^{2} = \frac{p ^{2}}{2 π ϵ _{0} m a ^{3}}

, so

v = \frac{p}{a} \frac{1}{2 π ϵ _{0} ma}

JEE Main · 2020 · 06 Sep 2020 · Shift 2 · Single correct option

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JEE Main · 2020 · 06 Sep 2020 · Shift 2 · Electrostatics

Solution

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