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?

For two equal and opposite charges placed at distance $d$, then electric field will be zero at

In which regions, electric field can be zero for given arrangement of an electron and two protons?

The linear charge density upon the semi-circular ring, on both side is same in magnitude, the electric field at $O$ is along

An infinite long thread carries a charge uniformly spread over its length. It is bent in the form as shown. If the charge per unit length is $\lambda$, the electric field at point $O$ is