$A$ closed surface passes through a spherical conductor as shown in the figure. If a negative charge $-Q$ is placed at point $P$,what will be the nature of the electric flux coming out of the closed surface?

The distribution of some charges on two Gaussian surfaces $A$ and $B$ are as shown in the figure. If $\phi_A$ and $\phi_B$ are electric fluxes linked with the surfaces $A$ and $B$ respectively,then $\frac{\phi_A}{\phi_B}=$

In a region of space,the electric field is given by $\vec E = 8\hat i + 4\hat j + 3\hat k$. The electric flux through a surface of area $100 \text{ units}$ in the $x-y$ plane is...

Which among the curves shown in the figure cannot possibly represent electrostatic field lines?

$A$ cubical region of side $a$ has its centre at the origin. It encloses three fixed point charges,$-q$ at $(0, -a/4, 0)$,$+3q$ at $(0, 0, 0)$,and $-q$ at $(0, +a/4, 0)$. Choose the correct option$(s)$.
$(A)$ The net electric flux crossing the plane $x = +a/2$ is equal to the net electric flux crossing the plane $x = -a/2$.
$(B)$ The net electric flux crossing the plane $y = +a/2$ is more than the net electric flux crossing the plane $y = -a/2$.
$(C)$ The net electric flux crossing the entire region is $\frac{q}{\varepsilon_0}$.
$(D)$ The net electric flux crossing the plane $z = +a/2$ is equal to the net electric flux crossing the plane $x = +a/2$.

$A$ square surface of side $L$ meters is in the plane of the paper. $A$ uniform electric field $\vec{E} \text{ (V/m)}$ is also in the plane of the paper,limited only to the lower half of the square surface. The electric flux associated with the surface in $SI$ units is: