Two electric dipoles $A, B$ with respective dipole moments $\overrightarrow {{d_A}} = - 4\,qa\,\hat i$ and $\overrightarrow {{d_B}} = 2\,qa\,\hat i$ 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
JEE MAIN 2019, Diffcult
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$v_{1}=v_{2}$
$\frac{\mathrm{k}(2 \mathrm{qa})}{\mathrm{x}^{2}}=\frac{\mathrm{k}(4 \mathrm{qa})}{(\mathrm{R}-\mathrm{x})^{2}}$
$R-x=\sqrt{2} x$
$x=\frac{R}{\sqrt{2}+1}$
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