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 $-Q$ at $(0, 0, -l)$. Take $2l \ll d$.
$R$. $E \propto \frac{1}{d^2}$ $3$. An infinite line charge coincident with the $x$-axis,with uniform linear charge density $\lambda$
$S$. $E \propto \frac{1}{d^3}$ $4$. Two infinite wires carrying uniform linear charge density parallel to the $x$-axis. The one along $(y=0, z=l)$ has a charge density $+\lambda$ and the one along $(y=0, z=-l)$ has a charge density $-\lambda$. Take $2l \ll d$
$5$. Infinite plane with uniform surface charge density

  • 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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