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

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Answer & Solution

Correct Answer

(A) \(\frac{{\sqrt 2 R}}{{\sqrt 2 + 1}}\)

Step-by-step Solution

Detailed explanation

\(v_{1}=v_{2}\)

\(\frac{\mathrm{k}(2 \mathrm{qa})}{\mathrm{x}^{2}}=\frac{\mathrm{k}(4 \mathrm{qa})}{(\mathrm{R}-\mathrm{x})^{2}}\)

\(R-x=\sqrt{2} x\)

\(x=\frac{R}{\sqrt{2}+1}\)

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