Match List - I with List - II.\\ $\begin{array}{l|l} \text{List - I} & \text{List - II} \\ \hline \text{(A)…

Match List - I with List - II.\\ $\begin{array}{l|l} \text{List - I} & \text{List - II} \\ \hline \text{(A) }\begin{array}{l} \text{Electric field inside} \\ \text{(distance } r > 0 \text{ from center)} \\ \text{of a uniformly charged} \\ \text{spherical shell with} \\ \text{surface charge density} \\ \sigma \text{, and radius } R. \end{array} & \text{(I)} \frac{\sigma}{\epsilon_0} \\ \text{(B)} \begin{array}{l} \text{Electric field at} \\ \text{distance } r > 0 \\ \text{from a uniformly} \\ \text{charged infinite plane} \\ \text{sheet with surface} \\ \text{charge density } \sigma. \end{array} & \text{(II)} \frac{\sigma}{2 \epsilon_0} \\ \text{(C)} \begin{array}{l} \text{Electric field outside} \\ \text{(distance } r > 0 \text{ from center)} \\ \text{of a uniformly charged} \\ \text{spherical shell with} \\ \text{surface charge density} \\ \sigma \text{, and radius } R. \end{array} & \text{(III)} 0 \\ \text{(D)} \begin{array}{l} \text{Electric field between} \\ 2 \text{ oppositely charged} \\ \text{infinite plane parallel} \\ \text{sheets with uniform} \\ \text{surface charge density } \sigma. \end{array} & \text{(IV)} \frac{\sigma R^{2}}{\epsilon_0 r^{2}} \end{array}$ Choose the correct answer from the options given below :
  1. (A)-(III), (B)-(II), (C)-(IV), (D)-(I)
  2. (A)-(IV), (B)-(II), (C)-(III), (D)-(I)
  3. (A)-(II), (B)-(I), (C)-(IV), (D)-(III)
  4. (A)-(IV), (B)-(I), (C)-(III), (D)-(II)

Solution

Inside uniformly charged spherical shell, $E=0$
$\therefore \mathrm{A} \rightarrow \mathrm{III}$
For uniformly charged infinite plate
$E=\frac{\sigma}{2 \varepsilon_0}$
$\therefore \mathrm{B} \rightarrow \mathrm{II}$
Outside of spherical shell
$E=\frac{Q}{4 \pi \varepsilon_0 r_2}=\frac{\sigma R^2}{\varepsilon_0 r^2}$
$\therefore \mathrm{C} \rightarrow \mathrm{IV}$
Between two plates $E=\frac{\sigma}{\varepsilon_0}$
$\therefore \mathrm{D} \rightarrow \mathrm{I}$

Asked in: JEE Main 2025 (29 Jan Shift 1)

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