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-$II$
$E$ is independent of $d$ A point charge $Q$ at the origin
$E \propto \frac{1}{d}$ A small dipole with point charges $Q$ at $(0,0, l)$ and $- Q$ at $(0,0,-l)$. Take $2 l \ll d$.
$E \propto \frac{1}{d^2}$ An infinite line charge coincident with the x-axis, with uniform linear charge density $\lambda$
$E \propto \frac{1}{d^3}$ 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 $2 l \ll d$
  plane with uniform surface charge density

 

  • [IIT 2018]
  • A

    $P \rightarrow 5 ; Q \rightarrow 3,4 ; R \rightarrow 1 ; S \rightarrow 2$

  • B

    $P \rightarrow 5 ; Q \rightarrow 3 ; R \rightarrow 1,4 ; S \rightarrow 2$

  • C

    $P \rightarrow 5 ; Q \rightarrow 3 ; R \rightarrow 1,2 ; S \rightarrow 4$

  • D

    $P \rightarrow 4 ; Q \rightarrow 2,3 ; R \rightarrow 1 ; S \rightarrow 5$

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