Two electric dipoles, A, B with respective dipole moments dA = -4qai… | JEE Main 2019 (10 Jan, Shift 1)

Q68JEE Main 2019 · 10 JAN · SHIFT 1Medium

Electric Dipole

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 -

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Answer: (c)

$V = \frac{k\,\vec p\cdot\hat r}{r^2}$ ; both moments point along $-x$ .
Between A and B the two potentials have opposite signs, so the point lies beyond B, at distance $x$ from A.
There $\frac{4qa}{x^2} = \frac{2qa}{(x - R)^2} \Rightarrow x = \sqrt2(x - R)$
$x = \frac{\sqrt2 R}{\sqrt2 - 1}$ , so the answer is (c).

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