Two identical electric point dipoles have dipole moments `vec(P_1) = p hati and vec(P_2) = 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 direaction of their dipole moments remaining unchanged. If the mass of each dipole is 'm', their speed when they are infinitely for apart is :

Options

A. Option1 `P/a sqrt(1/(pi in_0ma))`
B. Option2 `P/asqrt(1/(2piin_0ma))`
C. Option3 `P/asqrt(2/(2piin_0ma))`
D. Option4 `P/asqrt(3/(2piin_0ma))`

Explanation

To solve the problem, we need to analyze the motion of two identical electric dipoles that are initially at rest and then released. We will use the principles of electrostatics and energy conservation to find their speed when they are infinitely far apart.

### Step-by-Step Solution:

1. **Understanding the Dipoles**:
- We have two identical electric dipoles with dipole moments \(\vec{P_1} = p \hat{i}\) and \(\vec{P_2} = p \hat{i}\).
- They are placed on the x-axis at a distance \(a\) from each other.

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