Let be the uniform surface charge density of two infinite thin pl… - Vidyadip

MCQ

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
$\vec{E}_{ I }=\frac{2 \sigma}{\in_0} \hat{n}, \vec{E}_{ II }=0, \vec{E}_{ III }=\frac{2 \sigma}{\in_0} \hat{n}$
B
$\vec{E}_{ I }=0, \vec{E}_{ II }=\frac{\sigma}{\in_0} \hat{n}, \vec{E}_{ III }=0$
C
$\vec{E}_{ I }=\frac{\sigma}{2 \in_0} \hat{n}, \vec{E}_{\text {II }}=0, \vec{E}_{ III }=\frac{\sigma}{2 \in_0} \hat{n}$
✓
$\vec{E}_{ I }=-\frac{\sigma}{\in_0} \hat{n}, \vec{E}_{\text {II }}=0, \vec{E}_{\text {III }}=\frac{\sigma}{\in_0} \hat{n}$

✓

Answer

Correct option: D.

$\vec{E}_{ I }=-\frac{\sigma}{\in_0} \hat{n}, \vec{E}_{\text {II }}=0, \vec{E}_{\text {III }}=\frac{\sigma}{\in_0} \hat{n}$

d
Assuming RHS to be $\hat{n}$

$\vec{E}_{ I }=\frac{\sigma}{2 \in_0}(-\hat{n})+\frac{\sigma}{2 \in_0}(-\hat{n})=-\frac{\sigma}{\in_0} \hat{n}$

$\vec{E}_{I I}=0$,

$\vec{E}_{I I I}=\frac{\sigma}{2 \in_0}(\hat{n})+\frac{\sigma}{2 \in_0}(\hat{n})=\frac{\sigma}{\in_0}(\hat{n})$

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