Question 173 of 311

The distance between charges $+q$ and $-q$ is $2l$ and between $+2q$ and $-2q$ is $4l$. The electrostatic potential at point $P$ at a distance $r$ from centre $O$ is $-\alpha \left[\dfrac{ql}{{r}^{2}}\right]\times {10}^{9}V$, where the value of $\alpha$ is ______. (Use $\dfrac{1}{4\pi {\epsilon }_{0}}=9\times {10}^{9}N{m}^{2}{C}^{-2}$)

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Answer: 27

Considering two dipoles with charges 2q&q, we can write the equivalent setup as shown below:

Therefore, net dipole moment is ${P}_{net}=6ql$ in the leftward direction.

Potential required,
$V=\dfrac{K\vec{p}\cdot \vec{r}}{{r}^{3}} =\dfrac{9\times {10}^{9}\left(6ql\right)}{{r}^{2}}\cos \left({120}^{o}\right)$
$=-\left(27\right)\left(\dfrac{ql}{{r}^{2}}\right)\times {10}^{9}$
Therefore, $\alpha =27$.