A cylinder of height  $H$ ' and radius of cross-section $r$ ' is kept in uniform electric field $\overrightarrow{E}$ as shown in figure. The magnitude of flux that enters from left half of cylinder is

Use Gauss's Law to determine the electric field at$a.$

The "Gaussian Surface" for an infinitely large charged plate is pillbox of surface area A and length $2a$ centred about the origin. The plate has positive surface charge density $\sigma$.

Find the dipole-moment of system

Two molecule each with permanent dipole moment $\overrightarrow{p}$ are aligned as shown. Calculate the force between the molecules if they are separated by a distance that is large compared with the dimension of the dipoles.
[Hint : The relation $(1+x{)}^{-2}\cong 1-2x+3x^2-\dots \dots$ for small $x$ is useful].