JEE PYQ: Electrostatics Question 55
Question 55 - 2019 (10 Jan Shift 1)
Two electric dipoles, A, B with respective dipole moments $\vec{d}_A = -4qa\hat{i}$ and $\vec{d}_B = -2qa\hat{i}$ 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:
(1) $\frac{R}{\sqrt{2}+1}$
(2) $\frac{\sqrt{2}R}{\sqrt{2}+1}$
(3) $\frac{R}{\sqrt{2}-1}$
(4) $\frac{\sqrt{2}R}{\sqrt{2}-1}$
Show Answer
Answer: (4)
Solution
Let distance from B be $x$. From A it is $R + x$. $\frac{4qa}{(R+x)^2} = \frac{2qa}{x^2}$. $\frac{2}{(R+x)^2} = \frac{1}{x^2}$. $\sqrt{2}x = R + x$. $x = \frac{R}{\sqrt{2}-1}$. Distance from A $= R + x = R + \frac{R}{\sqrt{2}-1} = \frac{\sqrt{2}R}{\sqrt{2}-1}$.
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