Question

Three infinitely long charge sheets are placed as shown in the figure. The electric field at point $P$ is going to be

• A. $\frac{2\sigma }{{\epsilon }_0}\hat{k}$
• B. $-\frac{2\sigma }{{\epsilon }_0}\hat{k}$
• C. $\frac{4\sigma }{{\epsilon }_0}\hat{k}$
• D. $-\frac{4\sigma }{{\epsilon }_0}\hat{k}$

Answer 1

The correct option is B $-\frac{2\sigma }{{\epsilon }_0}\hat{k}$

$\text{Step 1: Electric field due to a large charged sheet}$ $\text{[Ref. Fig.]}$

Electric field due to the charged sheet with surface charge density $\sigma$ is $E=\frac{\sigma }{2{\epsilon }_0}$

Due to positve charge density field is away from sheet and due to negative charge density field is towards the sheet.

$\text{Step 2: Resultant field at point P}$

Electric field being a vector quantity, it will be added vectorially at a point.

${\overrightarrow{E}}_p={\overrightarrow{E}}_1+{\overrightarrow{E}}_2+{\overrightarrow{E}}_3$

$=\frac{\sigma }{2{\epsilon }_0}(-\hat{k})+\frac{-2\sigma }{2{\epsilon }_0}\left(\hat{k}\right)+\frac{-\sigma }{2{\epsilon }_0}\left(\hat{k}\right)$

$=\frac{-2\sigma }{{\epsilon }_0}\hat{k}$

Option $\left(B\right)$ correct answer.