Question

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

• A. $\frac{\sigma}{\in_{0}}\left[\left(1+\frac{\sqrt{3}}{2}\right)\widehat{y} + \frac{\widehat{x}}{2}\right]$
• B. $\frac{\sigma}{2\in_{0}}\left[\left(1+\sqrt{3}\right)\widehat{y} + \frac{\widehat{x}}{2}\right]$
• C. $\frac{\sigma}{2\in_{0}}\left[\left(1+\sqrt{3}\right)\widehat{y} - \frac{\widehat{x}}{2}\right]$
• D. $\frac{\sigma}{2\in_{0}}\left[\left(1-\frac{\sqrt{3}}{2}\right)\widehat{y} - \frac{\widehat{x}}{2}\right]$

Answer 1

Answer: (D)

$\vec{E}=\frac{\sigma}{2\varepsilon_{0}}cos\,60^{\circ}\left(-\hat{x}\right)+\left[\frac{\sigma }{2\varepsilon _{0}}-\frac{\sigma }{2\varepsilon _{0}}sin\,60^{\circ}\right]\left(\hat{y}\right)$
$\vec{E}=\frac{\sigma }{2\varepsilon _{0}}\left[\left(1-\frac{\sqrt{3}}{2}\right)\hat{y}-\frac{1}{2}\hat{x}\right]$