Two identical electric point dipoles have dipole moments vecP1=P hati and vecP2=-P hati 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 :

Question

Two identical electric point dipoles have dipole moments vecP1=P hati and vecP2=-P hati 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) ( p / a ) √(1/π ε0 ma ) (B)  ( p / a ) √(3/2 π ε0 ma ) (C) ( p / a ) √(1/2 π ε0 ma ) (D)  ( p / a ) √(2/π ε0 ma )

Tardigrade Admin · Accepted Answer

Using energy conservation: KE i+ PE i = KE f + PE f <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/88519f50e72a371a409c9b38970ff708-.png" /> O +(2 KP / a 3) × P =(1/2) mv 2 × 2+0 V =√(2 P 2/4 π ε0 a 3 m )=( P / a ) √(1/2 π ε0 am )

$\frac{p}{a} \frac{1}{π ε _{0} ma}$

$\frac{p}{a} \frac{3}{2 π ε _{0} ma}$

$\frac{p}{a} \frac{1}{2 π ε _{0} ma}$

$\frac{p}{a} \frac{2}{π ε _{0} ma}$

Using energy conservation:
$K E_{i} + P E_{i} = K E_{f} + P E_{f}$

$O + \frac{2 K P}{a ^{3}} \times P = \frac{1}{2} m v^{2} \times 2 + 0$
$V = \frac{2 P ^{2}}{4 π ε _{0} a ^{3} m} = \frac{P}{a} \frac{1}{2 π ε _{0} am}$

ap​πε0​ma1​​

ap​2πε0​ma3​​

ap​2πε0​ma1​​

ap​πε0​ma2​​

Using energy conservation: KEi​+PEi​=KEf​+PEf​ O+a32KP​×P=21​mv2×2+0 V=4πε0​a3m2P2​​=aP​2πε0​am1​​

$\frac{p}{a} \frac{1}{π ε _{0} ma}$

$\frac{p}{a} \frac{3}{2 π ε _{0} ma}$

$\frac{p}{a} \frac{1}{2 π ε _{0} ma}$

$\frac{p}{a} \frac{2}{π ε _{0} ma}$

Using energy conservation:
$K E_{i} + P E_{i} = K E_{f} + P E_{f}$

$O + \frac{2 K P}{a ^{3}} \times P = \frac{1}{2} m v^{2} \times 2 + 0$
$V = \frac{2 P ^{2}}{4 π ε _{0} a ^{3} m} = \frac{P}{a} \frac{1}{2 π ε _{0} am}$