Electrostatics

JEE Main level, single correct, medium

167 of 311

Question 167 of 311

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 (distance } r>0 \text { from center) } \\

\text { of a uniformly charged spherical shell with } \\

\text { surface charge density } \sigma \text {, and radius R. }

\end{array} & \text { (I) } \begin{array}{l}

\sigma / \epsilon_0

\end{array} \\

\text { (B) } \begin{array}{l}

\text { Electric field at distance r>0 from a uniformly } \\

\text { charged infinite plane sheet with surface } \\

\text { charge density } \sigma .

\end{array} & \text { (II) } \sigma / 2 \epsilon_0 \\

\text { (C) } \begin{array}{l}

\text { Electric field outside (distance r>0 from center) } \\

\text { of a uniformly charged 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 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 :

Show answer and solution

Answer: (A) (A)-(III), (B)-(II), (C)-(IV), (D)-(I)

Inside uniformly charged spherical shell, E=0E=0
∴A→III\therefore \mathrm{A} \rightarrow \mathrm{III}

For uniformly charged infinite plate

E=σ2ε0E=\frac{\sigma}{2 \varepsilon_0}
∴B→II\therefore \mathrm{B} \rightarrow \mathrm{II}

Outside of spherical shell

E=Q4πε0r2=σR2ε0r2E=\frac{Q}{4 \pi \varepsilon_0 r_2}=\frac{\sigma R^2}{\varepsilon_0 r^2}
∴C→IV\therefore \mathrm{C} \rightarrow \mathrm{IV}

Between two plates
E=σε0E=\frac{\sigma}{\varepsilon_0}
∴D→I\therefore \mathrm{D} \rightarrow \mathrm{I}

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