$A$ cylinder of radius $R$ and length $L$ is placed in a uniform electric field $E$ parallel to the cylinder axis. The total flux for the surface of the cylinder is given by-

$A$ hollow cylinder has a charge $q$ inside it. If $\phi$ is the electric flux associated with the curved surface $B$,the flux linked with the plane surface $A$ will be

The total electric flux through a closed spherical surface of radius $r$ enclosing an electric dipole of dipole moment $2aq$ is (Give $\varepsilon_0=$ permittivity of free space)

$A$ 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:-

If the electric flux entering and leaving an enclosed surface respectively is ${\varphi _1}$ and ${\varphi _2}$,the electric charge inside the surface will be:

$A$ thin spherical shell encloses a concentric solid sphere. The radius of the shell is $(0.060)^{1/2} \ m$ and its surface charge density is $-10^{-5} \ C/m^2$. The radius of the solid sphere is $(0.01)^{1/3} \ m$ and its volumetric charge density is $3 \times 10^{-5} \ C/m^3$. $\varepsilon_0$ is the permittivity of free space in $C^2/Nm^2$. The electric flux through a spherical surface concentric with the spherical shell and of radius greater than that of the shell in $V-m$ is: