Question

The infinitely long charged sheets are placed as shown in figure. The electric field at point $P$ is

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

For infinitely charged plane sheet, electric field is givenby,

$E=\frac{\sigma }{2{\epsilon }_0}$

Due to charge $+\sigma ,E_1=\frac{\sigma }{2{\epsilon }_0},$ downwards

Due to charge $+2\sigma ,E_2=\frac{2\sigma }{2{\epsilon }_0},$ downwards

Due to charge $-\sigma ,E_3=\frac{\sigma }{2{\epsilon }_0},$downwards

$\therefore$Total electric field at $P$.

$P=\frac{\sigma }{2{\epsilon }_0}+\frac{2\sigma }{2{\epsilon }_0}+\frac{\sigma }{2{\epsilon }_0}=\frac{2\sigma }{{\epsilon }_0},$ downwards

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