Question

A point charge of charge $q$ and mass $m$ is placed at rest at point $X$ at distance $r$ from a short electric dipole. The initial acceleration of charge $a=\frac{k \cdot q \cdot p}{2 m r^3} n$, where $k=\frac{1}{4 \pi \varepsilon_0}$. Then $n$ is (short electric dipole)

Answer 1

$a=\frac{F}{m}=\frac{E q}{m}=\left[\frac{1}{4 \pi \varepsilon_0} \frac{P \sqrt{3 \cos ^2 60^{\circ}+1}}{r^3}\right] \frac{q}{m}$
$=\frac{q}{m}\left[\frac{1}{4 \pi \varepsilon_0} \frac{P \sqrt{3\left(\frac{1}{2}\right)^2+1}}{r^3}\right]$
$=\frac{\sqrt{7}}{2}\left(\frac{1}{4 \pi \varepsilon_0}\right) \frac{q P}{m r^3} \text {. }$