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The electric field E at the point P(0,d) is measured for several charge distributions and its dependence on d differs. Match List-I (relation of E to d) with List-II (charge distributions). List-I: P. E independent of d Q. E proportional to 1/d R. E proportional to 1/d² S. E proportional to 1/d³ List-II: 1. A point charge Q at the origin 2. A small dipole: +Q at (0,0,l) and -Q at (0,0,-l), with 2l << d 3. An infinite line charge along the x-axis, linear density lambda 4. Two infinite parallel wires along the x-axis: +lambda at (y=0, z=l) and -lambda at (y=0, z=-l), with 2l << d 5. An infinite plane of charge in the xy-plane, surface density sigma
- P -> 5; Q -> 3, 4; R -> 1; S -> 2
- P -> 5; Q -> 3; R -> 1, 4; S -> 2
- P -> 5; Q -> 3; R -> 1, 2; S -> 4
- P -> 4; Q -> 2, 3; R -> 1; S -> 5
Correct answer: P -> 5; Q -> 3, 4; R -> 1; S -> 2
Solution
Infinite plane: field is constant, independent of d (P->5). Infinite line: E ~ 1/d (Q->3). Point charge: E ~ 1/d² (R->1). Small dipole: E ~ 1/d³ (S->2). The two opposite infinite wires form a configuration whose field falls as 1/d² faster than a single line; in the official JEE Advanced 2018 key this matches Q with both 3 and 4 in option A.
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