JEE PYQ: Electrostatics Question 29
Question 29 - 2020 (07 Jan Shift 1)
Two infinite planes each with uniform surface charge density $+\sigma$ are kept in such a way that the angle between them is $30°$. The electric field in the region shown between them is given by:
(1) $\frac{\sigma}{2\varepsilon_0}\left[(1+\sqrt{3})\hat{y} - \frac{\hat{x}}{2}\right]$
(2) $\frac{\sigma}{\varepsilon_0}\left[\left(1+\frac{\sqrt{3}}{2}\right)\hat{y} + \frac{\hat{x}}{2}\right]$
(3) $\frac{\sigma}{2\varepsilon_0}\left[(1+\sqrt{3})\hat{y} + \frac{\hat{x}}{2}\right]$
(4) $\frac{\sigma}{2\varepsilon_0}\left[\left(1-\frac{\sqrt{3}}{2}\right)\hat{y} - \frac{\hat{x}}{2}\right]$
Show Answer
Answer: (4)
Solution
$\vec{E_1} = \frac{\sigma}{2\varepsilon_0}\hat{y}$ (from horizontal plane). $\vec{E_2} = \frac{\sigma}{2\varepsilon_0}(-\cos 60°\hat{x} - \sin 60°\hat{y})$. $\vec{E_P} = \vec{E_1} + \vec{E_2} = \frac{\sigma}{2\varepsilon_0}\left[\left(1-\frac{\sqrt{3}}{2}\right)\hat{y} - \frac{\hat{x}}{2}\right]$.
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