The electric field in a region of space is given by $\vec{E} = (5\hat{i} + 2\hat{j}) \text{ N/C}$. Calculate the electric flux through a surface of area $2 \text{ m}^2$ lying in the $YZ$-plane.

Which of the following statements is correct?

Which of the following is a correct statement?

$A$ point charge $q$ is placed at a point inside a hollow conducting sphere. Which of the following electric force patterns is correct?

An infinitely long thin non-conducting wire is parallel to the $z$-axis and carries a uniform line charge density $\lambda$. It pierces a thin non-conducting spherical shell of radius $R$ in such a way that the arc $PQ$ subtends an angle $120^{\circ}$ at the centre $O$ of the spherical shell,as shown in the figure. The permittivity of free space is $\epsilon_0$. Which of the following statements is (are) true?
$(A)$ The electric flux through the shell is $\sqrt{3} R \lambda / \epsilon_0$
$(B)$ The $z$-component of the electric field is zero at all the points on the surface of the shell
$(C)$ The electric flux through the shell is $\sqrt{2} R \lambda / \epsilon_0$
$(D)$ The electric field is normal to the surface of the shell at all points

$A$ charge $q$ is placed inside a hollow cylinder. The electric flux associated with the curved surface $B$ is $\phi$. The flux associated with a plane surface (either $A$ or $C$) will be: