Question 114 of 311

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

A$\dfrac{\sigma }{2{\in }_{0}}\left[\left(1+\sqrt{3}\right)\hat{y}-\dfrac{\hat{x}}{2}\right]$B$\dfrac{\sigma }{{\in }_{0}}\left[\left(1+\dfrac{\sqrt{3}}{2}\right)\hat{y}+\dfrac{\hat{x}}{2}\right]$C$\dfrac{\sigma }{2{\in }_{0}}\left[\left(1+\sqrt{3}\right)\hat{y}+\dfrac{\hat{x}}{2}\right]$D$\dfrac{\sigma }{2{\in }_{0}}\left[\left(1-\dfrac{\sqrt{3}}{2}\right)\hat{y}-\dfrac{\hat{x}}{2}\right]$

Show answer and solution▾

Answer: (D) $\dfrac{\sigma }{2{\in }_{0}}\left[\left(1-\dfrac{\sqrt{3}}{2}\right)\hat{y}-\dfrac{\hat{x}}{2}\right]$

$\vec{E}=\dfrac{\sigma }{2{\epsilon }_{0}}\cos ⁡{60}^{o}\left(-\hat{x}\right)+\left[\dfrac{\sigma }{2{\epsilon }_{0}}-\dfrac{\sigma }{2{\epsilon }_{0}}\sin ⁡{60}^{o}\right]\left(\hat{y}\right)$
$\vec{E}=\dfrac{\sigma }{2{\epsilon }_{0}}\left[\left(1-\dfrac{\sqrt{3}}{2}\right)\hat{y}-\dfrac{1}{2}\hat{x}\right]$