When a $10 \mu C$ charge is enclosed by a closed surface,the flux passing through the surface is $\phi$. Now,another $10 \mu C$ charge is placed inside the closed surface,then the flux passing through the surface is . . . . . . .

If the radius of the spherical Gaussian surface is increased, then the electric flux due to a point charge enclosed by the surface

Eight dipoles of charges of magnitude $e$ are placed inside a cube. The total electric flux coming out of the cube will be

The figure shows the electric field lines for a system of two charges. Choose the correct option regarding the electric field intensity at points $A$,$B$,and $C$.

$A$ 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 $x = +a/2$.

Gauss's law should be invalid if