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Question:

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) E∝1/d (2) A small dipole with point charges Q at (0,0,l) and -Q at (0, 0, -l). Take 2l<<d (R) E∝1/d² (3) An infinite line charge coincident with the x-axis, with uniform linear charge density λ. (S) E∝1/d³ (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.

P→5;Q→3,4;R→1;S→2

P→5;Q→3;R→1,4;S→2

P→4;Q→2,3;R→1;S→5

P→5;Q→3;R→1,2;S→4

Solution:

The correct option is B
P→5;Q→3;R→1,4;S→2
(i) E =KQ/d² ⇒E∝1/d²
(ii) Dipole
E=2kp/d³√1+3cos²θ
E∝1/d³ for dipole
(iii) For line charge
E=2kλ/d
E∝1/d
(iv) E =2Kλd/(d²+l²)=2Kλ[d+l-d+l/d²-l²]
E=2Kλ(2l)/d²[1-l²/d²]
E∝1/d²
(v) Electric field due to sheet ε=σ/2ε₀
ε is independent of r