The electric field due to an infinitely long, straight line of charge with uniform charge density $\lambda$ points straight away from the line and has magnitude $E=\lambda /\left(2\mathrm{\pi }{\epsilon }_{0}r\right)$, where$r$ is the distance from the wire. Calculate the flux of this electric field through a right cylinder of height $h$ and radius $R$, co-axial with the charged line. Repeat the calculation for a cylinder of radius $2 R$.

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].

Two pith balls each with mass $m$ are suspended from insulating threads. When the pith balls are given equal positive charge $Q$, they hang in equilibrium as shown. We now increase the charge on the left pith ball from $Q$ to $2Q$ while leaving its mass essentially unchanged. Which of the following diagrams best represents the new equilibrium configuration?