Question

Let $\sigma$ be the uniform surface charge density of two infinite thin plane sheets shown in figure. Then the electric fields in three different region $E_I,E_{II}$ and $E_{III}$ are:

• A. ${\vec{E}}_I=0,{\vec{E}}_{II}=\frac{\sigma }{{ϵ}_0}\hat{n},E_{III}=0$
• B. ${\vec{E}}_I=\frac{2\sigma }{{ϵ}_0}\hat{n},{\vec{E}}_{II}=0,{\vec{E}}_{III}=\frac{2\sigma }{{ϵ}_0}\hat{n}$
• C. ${\vec{E}}_I=-\frac{\sigma }{{ϵ}_0}\hat{n},{\vec{E}}_{II}=0,{\vec{E}}_{III}=\frac{\sigma }{{ϵ}_0}\hat{n}$
• D. ${\vec{E}}_I=\frac{\sigma }{2{ϵ}_0}\hat{n},{\vec{E}}_{II}=0,{\vec{E}}_{III}=\frac{\sigma }{2{ϵ}_0}\hat{n}$

Answer 1

Answer: (C)

Assuming RHS to be $\hat{n}$
${\vec{E}}_I=\frac{\sigma }{2{ϵ}_0}(-\hat{n})+\frac{\sigma }{2{ϵ}_0}(-\hat{n})=-\frac{\sigma }{{ϵ}_0}\hat{n}$
${\vec{E}}_{II}=0$
${\vec{E}}_{III}=\frac{\sigma }{2{ϵ}_0}(\hat{n})+\frac{\sigma }{2{ϵ}_0}(\hat{n})=\frac{\sigma }{{ϵ}_0}(\hat{n})$