Question

Two electric dipoles, $A, B$ with respective dipole moments $\vec{d}_A = - 4 \,qa \,\hat{i}$ and $\vec{d}_B = - 2 \,qa\, \hat{i}$ 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

Answer: (C)

$\frac{\sqrt{2}R}{\sqrt{2} - 1}$

Answer 2

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