Column $II$ corresponds to the graph of magnitude of electric field versus distance from the centre of the charge distribution in Column $I$. Match the items in Column $I$ with the corresponding graphs in Column $II$.
Column-$I$ Column-$II$ $(A)$ Ring along its axis $(P)$ Graph with a peak at a distance $r > 0$ $(B)$ Uniformly charged solid sphere $(Q)$ Graph increasing linearly for $r < R$ and decreasing as $1/r^2$ for $r > R$ $(C)$ Uniformly charged spherical shell $(R)$ Graph with zero field for $r < R$ and decreasing as $1/r^2$ for $r > R$ $(D)$ Combination of charge $+Q$ and $-Q$ at the perpendicular bisector $(S)$ Graph with a maximum at the center and decreasing as $r$ increases
| Column-$I$ | Column-$II$ |
|---|---|
| $(A)$ Ring along its axis | $(P)$ Graph with a peak at a distance $r > 0$ |
| $(B)$ Uniformly charged solid sphere | $(Q)$ Graph increasing linearly for $r < R$ and decreasing as $1/r^2$ for $r > R$ |
| $(C)$ Uniformly charged spherical shell | $(R)$ Graph with zero field for $r < R$ and decreasing as $1/r^2$ for $r > R$ |
| $(D)$ Combination of charge $+Q$ and $-Q$ at the perpendicular bisector | $(S)$ Graph with a maximum at the center and decreasing as $r$ increases |
- A$(A)-(Q); (B)-(S); (C)-(R); (D)-(P)$
- B$(A)-(S); (B)-(R); (C)-(P); (D)-(S)$
- C$(A)-(R); (B)-(P); (C)-(Q); (D)-(R)$
- D$(A)-(P); (B)-(Q); (C)-(S); (D)-(R)$
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|---|---|
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| $Q$. $E \propto \frac{1}{d}$ | $2$. $A$ small dipole with point charges $Q$ at $(0, 0, l)$ and $-Q$ at $(0, 0, -l)$. Take $2l \ll d$. |
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| $S$. $E \propto \frac{1}{d^3}$ | $4$. 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 |
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