JEE MAIN - Physics (2020 - 6th September Evening Slot - No. 23)
Two identical electric point dipoles have dipole moments $${\overrightarrow p _1} = p\widehat i$$ and $${\overrightarrow p _2} = - p\widehat i$$ 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 :
$${p \over a}\sqrt {{3 \over {2\pi { \in _0}ma}}} $$
$${p \over a}\sqrt {{1 \over {\pi { \in _0}ma}}} $$
$${p \over a}\sqrt {{1 \over {2\pi { \in _0}ma}}} $$
$${p \over a}\sqrt {{2 \over {\pi { \in _0}ma}}} $$
Explanation
_6th_September_Evening_Slot_en_23_1.png)
Using energy conservation :
KEi + PEi = KEf + PEf
0 + $${{2KP} \over {{a^3}}} \times P$$ = $${1 \over 2}m{v^2} \times 2 + 0$$
$$ \Rightarrow $$ v = $$\sqrt {{{2{P^2}} \over {4\pi {\varepsilon _0}{a^3}m}}} $$
= $${P \over a}\sqrt {{1 \over {2\pi {\varepsilon _0}am}}} $$
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