Question 263 of 311

Two electric dipoles, $A,$ $B$ with respective dipole moments $\vec{{d}_{A}}=-4qa\hat{i}$ and $\vec{{d}_{B}}=-2qa\hat{i}$ are placed on the $x$ -axis with a separation $R,$ as shown in the figure



The distance from $A$ at which both of them produce the same potential is:

A$\dfrac{R}{\sqrt{2}-1}$B$\dfrac{\sqrt{2}R}{\sqrt{2}-1}$C$\dfrac{\sqrt{2}R}{\sqrt{2}+1}$D$\dfrac{R}{\sqrt{2}+1}$

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Answer: (B) $\dfrac{\sqrt{2}R}{\sqrt{2}-1}$

${V}_{1}+{V}_{2}=0$

$\dfrac{K4qa}{{x}^{2}}-\dfrac{K2qa}{{\left(x-R\right)}^{2}}=0$

${x}^{2}=2{\left(x-R\right)}^{2}$

$x=\left(\dfrac{\sqrt{2}R}{\sqrt{2}-1}\right)$