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. $\frac{\sigma }{{\in }_0}\left[\left(1+\frac{\sqrt{3}}{2}\right)\hat{y}+\frac{\hat{x}}{2}\right]$
• B. $\frac{\sigma }{2{\in }_0}\left[\left(1+\sqrt{3}\right)\hat{y}+\frac{\hat{x}}{2}\right]$
• C. $\frac{\sigma }{2{\in }_0}\left[\left(1+\sqrt{3}\right)\hat{y}-\frac{\hat{x}}{2}\right]$
• D. $\frac{\sigma }{2{\in }_0}\left[\left(1-\frac{\sqrt{3}}{2}\right)\hat{y}-\frac{\hat{x}}{2}\right]$

Answer 1

Answer: (D)

$\vec{E}=\frac{\sigma }{2{\epsilon }_0}cos60^{\circ }\left(-\hat{x}\right)+\left[\frac{\sigma }{2{\epsilon }_0}-\frac{\sigma }{2{\epsilon }_0}sin60^{\circ }\right]\left(\hat{y}\right)$
$\vec{E}=\frac{\sigma }{2{\epsilon }_0}\left[\left(1-\frac{\sqrt{3}}{2}\right)\hat{y}-\frac{1}{2}\hat{x}\right]$