Question

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

A
2σε0^k
B
2σε0^k
C
4σε0^k
D
4σε0^k

Solution

## The correct option is B $$-\cfrac { 2\sigma }{ { \varepsilon }_{ 0 } } \hat { k }$$$$\textbf{Step 1: Electric field due to a large charged sheet}$$ $$\textbf{[Ref. Fig.]}$$Electric field due to the charged sheet with surface charge density $$\sigma$$ is $$E = \cfrac{\sigma }{{2{\varepsilon _0}}}$$Due to positve charge density field is away from sheet and due to negative charge density field is towards the sheet.$$\textbf{Step 2: Resultant field at point P}$$Electric field being a vector quantity, it will be added vectorially at a point.                 $$\vec{E}_p = \vec{E}_1 + \vec{E}_2 + \vec{E}_3$$                       $$= \dfrac{\sigma}{2 \varepsilon_0} (-\hat{k}) + \dfrac{-2 \sigma}{2 \varepsilon_0} (\hat{k}) + \dfrac{-\sigma}{2 \varepsilon_0} (\hat{k})$$                       $$= \dfrac{-2 \sigma }{\varepsilon_0} \hat{k}$$Option $$(B)$$ correct answer.Physics

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