question_answer

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

A) \[\frac{2\sigma }{{{\varepsilon }_{0}}}\hat{k}\]  

B)        \[\frac{4\sigma }{{{\varepsilon }_{0}}}\hat{k}\]

C) \[-\frac{2\sigma }{{{\varepsilon }_{0}}}\hat{k}\] 

D)        \[-\frac{4\sigma }{{{\varepsilon }_{0}}}\hat{k}\]

Correct Answer: C

Solution :

[c] Figure shows the electric fields due to the sheets 1, 2 and 3 at point-P. The direction of electric fields are according to the charge on the sheets (away from positively charge sheet and towards the negatively charged sheet and perpendicular). The total electric field \[\overrightarrow{E}={{\overrightarrow{E}}_{1}}+{{\overrightarrow{E}}_{2}}+{{\overrightarrow{E}}_{3}}\] \[={{E}_{1}}(-\hat{k})+{{E}_{2}}(-\hat{k})+{{E}_{3}}(-\hat{k})\] \[=\left[ \frac{\sigma }{2{{\varepsilon }_{0}}}+\frac{2\sigma }{2{{\varepsilon }_{0}}}+\frac{\sigma }{2{{\varepsilon }_{0}}} \right](-\hat{k})=-\frac{2\sigma }{{{\varepsilon }_{0}}}\hat{k}\]