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

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 $2 l \ll d$
(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 $2 l \ll d$
(5) Infinite plane charge coincident with the $xy$-plane with uniform surface charge density

Accepted Answer

(B) $\mathrm{P} \rightarrow 5 ; \quad \mathrm{Q} \rightarrow 3 ; \quad \mathrm{R} \rightarrow 1,4 ; \quad \mathrm{S} \rightarrow 2$

Answer

(A) $\mathbf{P} \rightarrow \mathbf{5} ; \quad \mathbf{Q} \rightarrow \mathbf{3}, \mathbf{4} ; \quad \mathbf{R} \rightarrow \mathbf{1} ; \quad \mathbf{S} \rightarrow \mathbf{2}$

Answer

(C) $\mathbf{P} \rightarrow \mathbf{5} ; \quad \mathbf{Q} \rightarrow \mathbf{3} ; \quad \mathbf{R} \rightarrow \mathbf{1}, \mathbf{2} ; \mathbf{S} \rightarrow \mathbf{4}$

Answer

(D) $\mathrm{P} \rightarrow 4 ; \quad \mathrm{Q} \rightarrow 2,3 ; \quad \mathrm{R} \rightarrow 1 ; \quad \mathrm{S} \rightarrow 5$

JEE Advanced · 2018 · 20 May 2018 · Paper 2 · Electrostatics

Solution

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