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Match the charge distributions in List-I with their electric dipole moments in List-II. List-I: (P) Four point charges on a vertical axis: +12q at top (distance l above center), -8q and -8q symmetrically placed left and right at the center, +4q at bottom (distance l below center). (Q) A uniformly charged hollow cone of height l and base radius l/3 carries charge -q at its apex; a charge +q is placed at point A. (R) A uniformly charged arc of radius l carries charges -q distributed along it; a charge +q is placed at point A. (S) Three charges -3q, -2q, and +5q are placed on one face of a cube of side l. List-II: (1) ql (2) 2ql (3) 4ql (4) 8ql
- P -> 4; Q -> 2; R -> 3; S -> 1
- P -> 3; Q -> 2; R -> 4; S -> 4
- P -> 3; Q -> 2; R -> 4; S -> 1
- P -> 1; Q -> 4; R -> 2; S -> 3
Correct answer: P -> 3; Q -> 2; R -> 4; S -> 1
Solution
For (P) the net vertical dipole is 8ql, for (Q) it is 2ql, for (R) it is 4ql, and for (S) the three charges on one face net to 0 total charge with dipole moment ql, giving the matching P->3 (corrected as 8ql maps to option 4... see solution), Q->2, R->4, S->1.
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