In a region,the intensity of an electric field is given by $\overrightarrow{E}=(2 \hat{i}+3 \hat{j}+\hat{k}) \text{ NC}^{-1}$. The electric flux through a surface of area $10 \hat{i} \text{ m}^2$ in the region is

If the electric flux entering and leaving an enclosed surface is $\phi_1$ and $\phi_2$ respectively, then the charge enclosed in the surface is ($\varepsilon_0 =$ permittivity of free space).

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

Three positive charges of equal value $q$ are placed at the vertices of an equilateral triangle. The resulting lines of force should be sketched as in:

If $\oint_s \vec{E} \cdot \overrightarrow{d S}=0$ over a surface,then:

An electric dipole is placed in the north-south direction inside a sphere filled with water. Which statement is correct?