Two electric dipoles, A , B with respective dipole moments d A → = - 4 q a i ^ and d B → = - 2 q…

Two electric dipoles, $A,$ $B$ with respective dipole moments $\overrightarrow{d_A}=-4qa\widehat{\mathrm{i}}$ and $\overrightarrow{d_B}=-2qa\widehat{\mathrm{i}}$ 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:

1. $\frac{R}{\sqrt{2 }-1}$
2. $\frac{\sqrt{2}R}{\sqrt{2}-1}$
3. $\frac{\sqrt{2} R}{\sqrt{2}+1}$
4. $\frac{R}{\sqrt{2}+1}$

Solution

$V_1+V_2=0$

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

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

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

Asked in: JEE Main 2019 (10 Jan Shift 1)

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