Question

Two infinite uniform sheet of charge each with surface charge density $\sigma$ are located at $x=a$ and $x=-a$. Which of the following is correct?

• A. $E=\frac{-\sigma }{{ϵ}_0}\overrightarrow{i}$ ; For $x<-a$
• B. $E=0$ ; For $-a<x<a$
• C. $E=\frac{\sigma }{{ϵ}_0}\overrightarrow{i}$ ; For $x>a$
• D. $E=\frac{2\sigma }{{ϵ}_0}\overrightarrow{i}$ ; For $-a<x<a$

Answer 1

Answer: (A), (B), (C)

The correct options are
A $E=\frac{-\sigma }{{ϵ}_0}\overrightarrow{i}$ ; For $x<-a$
B $E=0$ ; For $-a<x<a$
C $E=\frac{\sigma }{{ϵ}_0}\overrightarrow{i}$ ; For $x>a$

At (1) $\overrightarrow{E}=\frac{\sigma }{2{\epsilon }_0}+\frac{\sigma }{2{\epsilon }_0}$ {due to sheet A & B}

$=\frac{\sigma }{{\epsilon }_0}=\frac{\sigma }{{\epsilon }_0}\{-i\}$ (directed toward -ve x-axis)

Similarly, at (3) $\overrightarrow{E}=\frac{\sigma }{2{\epsilon }_0}+\frac{\sigma }{2{\epsilon }_0}$ {due to sheet A & B}

$=\frac{\sigma }{{\epsilon }_0}\left(i\right)$ (directed towards +ve x-axis)

But at (2), $\overrightarrow{E}=\frac{\sigma }{2{\epsilon }_0}-\frac{\sigma }{2{\epsilon }_0}$ {due to opposite direction at electric field}

$=0$

$\therefore$ Option (A), (B) & (C) satisfy the equ. (1), (2) & (3) respectively.

That is why (A), (B) & (C) are correct answer.