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∝1d | (2) A small dipole with point charges Q at (0,0,l) and - Q at (0, 0, -l). Take 2l<<d |
(R) E∝1d2 | (3) A infinite line charge coincident with the x-axis, with uniform linear charge density λ. |
(S) E∝1d3 | (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. |
(i) E = KQd2⇒E∝1d2
(ii) Dipole
E=2kpd3√1+3cos2θ
E∝1d3 for dipole
(iii) For line charge
E=2kλd
E∝1d
(iv) E = 2Kλd−1−2Kλd+l
=2Kλ[d+l−d+ld2–l2]
E=2Kλ(2l)d2[1−l2d2]
E∝1d2
(v) Electric field due to sheet
ϵ=σ2ϵ0
ϵ is independent of r