Physics - Electrostatics Question with Solution | TestHub

Electric flux, $\mathbf{E}\cdot \mathbf{S}$, or $\varphi =ES\cos \theta$ Here, $\theta$ is the angle between $\mathbf{E}$ and $\mathbf{S}$. In this question $\theta =45^{\circ }$, because $\mathbf{S}$ is perpendicular to the surface. $$\begin{array}{c}E=E_0\\ \Rightarrow S=(\sqrt{2a})(a)=\sqrt{2}{a}^2\\ \therefore \varphi =\left(E_0\right)\left(\sqrt{2}{a}^2\right)\cos 45^{\circ }=E_0{a}^2\end{array}$$ $\therefore$ Correct option is (c). Analysis of Question (i) Question is moderately tough. (ii) The given shaded area is a rectangle not a square. One side of this rectangle is $a$ and other side is $\sqrt{2}a$. (iii) Electric field is uniform, whose magnitude is $E_0$ and direction is positive $x$. In uniform electric field we can use, $\varphi =ES\cos \theta$