A dipole of dipole moment $\vec{p} = p \hat{i}$ is kept at the centre of a circle of radius r as shown in the figure. The radius of the circle is very large in comparison to the distance between the two charges of the dipole. A & B are two points on the axis and C & D are two points on the equatorial line of the dipole. If $V_{A}, V_{B}, V_{C}$ and $V_{D}$ are potentials at A, B, C and D respectively, then which of the following is CORRECT?

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$V_{A} - V_{B} = \frac{2 k p}{r^{2}}, V_{A} - V_{D} = \frac{- k p}{r^{2}}$

$V_{A} - V_{B} = 0, V_{A} - V_{D} = \frac{k p}{r^{2}}$

$V_{A} - V_{B} = \frac{2 k p}{r^{2}}, V_{A} - V_{D} = \frac{k p}{r^{2}}$

$V_{A} - V_{B} = 0, V_{A} - V_{D} = \frac{2 k p}{r^{2}}$

answer is C.

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Detailed Solution

$V = \frac{k P \cos θ}{r^{2}}$

$V = \frac{k P \cos θ}{r^{2}} B \to θ = 180 ° C, D \to θ = 90 °$

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