${q_1},\;{q_2},\;{q_3}$ and ${q_4}$ are point charges located at points as shown in the figure and $S$ is a spherical Gaussian surface of radius $R$. Which of the following is true according to the Gauss’s law
$\oint_s {({{\vec E}_1} + {{\vec E}_2} + {{\vec E}_3}).d\vec A} = \frac{{{q_1} + {q_2} + {q_3}}}{{2{\varepsilon _0}}}$
$\oint_s {({{\vec E}_1} + {{\vec E}_2} + {{\vec E}_3}).d\vec A} = \frac{{({q_1} + {q_2} + {q_3})}}{{{\varepsilon _0}}}$
$\oint_s {({{\vec E}_1} + {{\vec E}_2} + {{\vec E}_3}).d\vec A} = \frac{{({q_1} + {q_2} + {q_3} + {q_4})}}{{{\varepsilon _0}}}$
None of the above
A charge $Q$ is placed at a distance $a/2$ above the centre of the square surface of edge $a$ as shown in the figure. The electric flux through the square surface is
A charged particle $q$ is placed at the centre $O$ of cube of length $L$ $(A\,B\,C\,D\,E\,F\,G\,H)$. Another same charge $q$ is placed at a distance $L$ from $O$.Then the electric flux through $BGFC$ is
The electric field intensity at $P$ and $Q$, in the shown arrangement, are in the ratio
The electric field in a region is given by $\overrightarrow{ E }=\frac{2}{5} E _{0} \hat{ i }+\frac{3}{5} E _{0} \hat{ j }$ with $E _{0}=4.0 \times 10^{3}\, \frac{ N }{ C } .$ The flux of this field through a rectangular surface area $0.4 \,m ^{2}$ parallel to the $Y - Z$ plane is ....... $Nm ^{2} C ^{-1}$
A few electric field lines for a system of two charges $Q_1$ and $Q_2$ fixed at two different points on the $x$ -axis are shown in the figure. These lines suggest that:-