$A$ 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

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

The figure shows the electric field lines around three point charges $A, B$,and $C$.
$(a)$ Which charges are positive?
$(b)$ Which charge has the largest magnitude? Why?
$(c)$ In which region or regions of the picture could the electric field be zero? Justify your answer.
$(i)$ Near $A$ $(ii)$ Near $B$ $(iii)$ Near $C$ $(iv)$ Nowhere

An electrostatic field line leaves at an angle $\alpha$ from a point charge $q_{1}$ and connects with a point charge $-q_{2}$ at an angle $\beta$ ($q_{1}$ and $q_{2}$ are positive). See the figure below. If $q_{2} = \frac{3}{2} q_{1}$ and $\alpha = 30^{\circ}$,then:

In a uniform electric field,a cube of side $1 \ cm$ is placed. The total energy stored in the cube is $8.85 \ \mu J$. The electric field is parallel to four of the faces of the cube. The electric flux through any one of the remaining two faces is

$A$ 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