JEE Advanced 2018 · Paper 2 · Physics Q15

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PhysicsList match+3 / -1Question 15 of 54

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

P
$E$ is independent of $d$
Q
$E \propto \dfrac{1}{d}$
R
$E \propto \dfrac{1}{d^2}$
S
$E \propto \dfrac{1}{d^3}$

LIST-II

1
A point charge $Q$ at the origin
2
A small dipole with point charges $Q$ at $(0, 0, l)$ and $-Q$ at $(0, 0, -l)$ . Take $2l \ll d$
3
An infinite line charge coincident with the $x$ -axis, with uniform linear charge density $\lambda$
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 $+\lambda$ and the one along $(y = 0, z = -l)$ has a charge density $-\lambda$ . Take $2l \ll d$
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 → 5; Q → 3; R → 1, 2; S → 4

P → 4; Q → 2, 3; R → 1; S → 5

Answer and worked solution

Official answer: B

Field at $(0,0,d)$ for each distribution:

Point charge: $E=\dfrac{kQ}{d^2}\propto\dfrac1{d^2}$ .
Small dipole along $z$ , on its axis: $E=\dfrac{2k(2lQ)}{d^3}\propto\dfrac1{d^3}$ .
Infinite line along $x$ , a distance $d$ away: $E=\dfrac\lambda{2\pi\epsilon_0d}\propto\dfrac1d$ .
Two opposite lines a distance $2l$ apart (a line dipole): the $1/d$ terms cancel, leaving $E\approx\dfrac{\lambda(2l)}{2\pi\epsilon_0d^2}\propto\dfrac1{d^2}$ .
Infinite plane: $E=\dfrac\sigma{2\epsilon_0}$ , independent of $d$ .

Match. P → 5; Q → 3; R → 1, 4; S → 2.

(B)

Topics:Electric field Electric dipole Electric flux and Gauss's law

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JEE Advanced 2018 · Paper 2, Physics question 15