Two infinite sheets each with uniform charge density $+ σ$ are kept in such a way that the angle between them is $30^{0}$ . The electric field in the region shown between them is given by:

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$\frac{σ}{2 ε_{0}} [(1 + \sqrt{3}) \hat{y} - \frac{\hat{x}}{2}]$

$\frac{σ}{2 ε_{0}} [(1 - \frac{\sqrt{3}}{2}) \hat{y} - \frac{\hat{x}}{2}]$

$\frac{σ}{ε_{0}} [(1 + \frac{\sqrt{3}}{2}) \hat{y} + \frac{\hat{x}}{2}]$

$\frac{σ}{2 ε_{0}} [(1 + \sqrt{3}) \hat{y} + \frac{\hat{x}}{2}]$

answer is B.

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Detailed Solution

Electric field due to infinite sheet $\bar{E} = \frac{σ}{2 ε_{0}} \hat{n}$

${\hat{E}}_{1} = - \cos 60^{0} \hat{x} - \sin 60^{0} \hat{y}$

$= - \frac{\hat{x}}{2} - \frac{\sqrt{3}}{2} \hat{y} {\hat{E}}_{_{2}} = \frac{σ}{2 ε_{0}} \hat{y} \bar{E_{1}} + \bar{E_{2}} = \frac{σ}{2 ε_{0}} \hat{E} + \frac{σ}{2 ε_{0}} {\hat{E}}_{_{L}} = \frac{σ}{2 ε_{0}} [(1 - \frac{\sqrt{3}}{2}) \hat{y} - \frac{\hat{x}}{2}]$