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Question

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

1022246_ca08b542b72f453d8cdeb9274d447338.png


A
2σε0^k
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B
2σε0^k
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C
4σε0^k
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D
4σε0^k
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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.

2113208_1022246_ans_fa36f926298549d89553c2221547257d.png

Physics

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