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The electric field E is measured at a point P(0, 0, d) generated due to various charge distributions and the dependence of E on d is found to be different for different charge distributions. List - I contains different relations between E and d. List - II describes different electric charge distributions, along with their locations. Match the functions in List - I with the related charge distributions in List - II
List - I List - II
(P) E is independent of d (1) A point charge Q at the origin
(Q) E1d (2) A small dipole with point charges Q at (0,0,l) and - Q at (0,0,l). Take 2l<<d
(R) E1d2 (3) A infinite line charge coincident with the x-axis, with uniform linear charge density λ.
(S) E1d3 (4) Two infinite wires carrying uniform linear charge density parallel to the x-axis. The one along (y=0,z=l) has a charge density + λ and the one along (y=0,z=l) has a charge density λ. Take 2l<<d
(5) Infinite plane charge coincident with the xy-plane with uniform surface charge density

A
P5;Q3,4;R1;S2
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B
P5;Q3;R1,4;S2
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C
P5;Q3;R1,2;S4
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D
P4;Q2,3;R1;S5
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Solution

The correct option is B P5;Q3;R1,4;S2
(1) E = KQd2E1d2

(2) Dipole
E=2kpd31+3cos2θ
E1d3 for dipole

(3) For line charge
E=2kλd
E1d

(4) E = 2Kλdl2Kλd+l
=2Kλ[d+ld+ld2l2]
E=2Kλ(2l)d2[1l2d2]
E1d2

(5) Electric field due to sheet
E=σ2ϵ0
E is independent of d

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