The electric field E is measured at a point P0,0,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-ILIST-IIP) E is independent of d1) A point charge Q at the originQ) E∝1d2) A small dipole with point charges Q at 0,0,l and - 0,0,−l Take 2l<<dR) E∝1d23) An infinite line charge coincident with the x-axis, with uniform linear charge density λ S) E∝1d34) 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=2kpd31+3cos2θ ⇒E∝1d3 (iii) for line charge E=2kλd ⇒E∝1d (iv) E=2Kλd−l−2Kλd+l ⇒E=2Kld+l−d+ld2−l2=2Kld2−l2 ⇒E∝1d2 (V) Electric filed due to sheet E=σ2∈0 E is independent of d

The electric field E is measured at a point P0,0,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-ILIST-IIP) E is independent of d1) A point charge Q at the originQ) E∝1d2) A small dipole with point charges Q at 0,0,l and - 0,0,−l Take 2l<<dR) E∝1d23) An infinite line charge coincident with the x-axis, with uniform linear charge density λ S) E∝1d34) 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=2kpd31+3cos2θ ⇒E∝1d3 (iii) for line charge E=2kλd ⇒E∝1d (iv) E=2Kλd−l−2Kλd+l ⇒E=2Kld+l−d+ld2−l2=2Kld2−l2 ⇒E∝1d2 (V) Electric filed due to sheet E=σ2∈0 E is independent of d

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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) $E \propto \frac{1}{d}$ 2) A small dipole with point charges Q at $(0, 0, l)$ and - $(0, 0, - l)$ Take $2 l < < d$
R) $E \propto \frac{1}{d^{2}}$ 3) An infinite line charge coincident with the x-axis, with uniform linear charge density $λ$
S) $E \propto \frac{1}{d^{3}}$ 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 $2 l < < d$
5) Infinite plane charge coincident with the xy-plane with uniform surface charge density

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P → 5; Q → 3; R → 1, 2; S → 4

P → 5; Q → 3, 4; R → 1; S → 2

P → 4; Q → 2, 3; R → 1; S → 5

P → 5; Q → 3; R → 1, 4; S → 2

answer is B.

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Detailed Solution

(i) $E = \frac{K Q}{d^{2}}$

$\Rightarrow E \propto \frac{1}{d^{2}}$

(ii) dipole
$E = \frac{2 k p}{d^{3}} \sqrt{1 + 3 \cos^{2} θ}$

$\Rightarrow E \propto \frac{1}{d^{3}}$
(iii) for line charge $E = \frac{2 k λ}{d}$

$\Rightarrow E \propto \frac{1}{d}$
(iv) $E = \frac{2 K λ}{d - l} - \frac{2 K λ}{d + l}$

$\Rightarrow E = 2 K l [\frac{d + l - d + l}{d^{2} - l^{2}}] = \frac{2 K l}{d^{2} - l^{2}}$
$\Rightarrow E \propto \frac{1}{d^{2}}$
(V) Electric filed due to sheet

$E = \frac{σ}{2 \in_{0}}$

$E$ is independent of d

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