A small dipole of dipole moment \overset{\rightarrow}{p} (directed along – ve x - axis) and length ℓ is placed with its centre at origin. Consider an imaginary sphere of radius R, where R >> ℓ. Match the value of electric field in column I with the locus in column II. Column - I Column - II (A) \left|\right. \overset{\rightarrow}{E} \left|\right. = \frac{k \left|\right. \overset{\rightarrow}{p} \left|\right.}{R^{3}} (P) One circle on the surface of sphere (B) \left|\right. \overset{\rightarrow}{E} \left|\right. = \frac{3}{2} \frac{k \left|\right. \overset{\rightarrow}{p} \left|\right.}{R^{3}} (Q) Two points on the surface of sphere (C) \left|\right. \overset{\rightarrow}{E} \left|\right. = \frac{3 k \left|\right. \overset{\rightarrow}{p} \left|\right.}{R^{3}} (R) Two circles on the surface of sphere (S) No point on the sphere

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Question

A small dipole of dipole moment $\vec{p}$ (directed along – ve x - axis) and length ℓ is placed with its centre at origin. Consider an imaginary sphere of radius R, where R >> ℓ. Match the value of electric field in column I with the locus in column II.

Column - I	Column - II
(A) $\| \vec{E} \| = \frac{k \| \vec{p} \|}{R^{3}}$	(P) One circle on the surface of sphere
(B) $\| \vec{E} \| = \frac{3}{2} \frac{k \| \vec{p} \|}{R^{3}}$	(Q) Two points on the surface of sphere
(C) $\| \vec{E} \| = \frac{3 k \| \vec{p} \|}{R^{3}}$	(R) Two circles on the surface of sphere
	(S) No point on the sphere

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