Question

Two electric dipoles, $A,B$ with respective dipole moments ${\overrightarrow{d}}_A=-4qa\hat{i}$ and ${\overrightarrow{d}}_B=-2qa\hat{i}$ 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. $\frac{\sqrt{2}R}{\sqrt{2}+1}$
• B. $\frac{R}{\sqrt{2}+1}$
• C. $\frac{\sqrt{2}R}{\sqrt{2}-1}$
• D. $\frac{R}{\sqrt{2}-1}$

Answer 1

The correct option is C $\frac{\sqrt{2}R}{\sqrt{2}-1}$

$V=\frac{4qa}{(R+x)}=\frac{2qa}{\left(x^2\right)}$
$\sqrt{2}x=R+x$
$x=\frac{R}{\sqrt{2}-1}$
$distance=\frac{R}{\sqrt{2}-1}+R=\frac{\sqrt{2}R}{\sqrt{2}-1}$.