Q. 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 :

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Solution:

$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}$

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