Two charges $+q$ and $-q$ are kept at a certain distance apart. Then, at any point on the perpendicular bisector of the line joining the two charges:

$A$ molecule of a substance has a permanent electric dipole moment of magnitude $10^{-29} \text{ C m}$. $2 \text{ mole}$ of this substance is polarized (at low temperature) by applying a strong electrostatic field of magnitude $10^6 \text{ V m}^{-1}$. What is the potential energy of the system? ($1 \text{ mole}$ of substance contains $6 \times 10^{23}$ molecules.)

An electric dipole with dipole moment $\vec{p} = \frac{p_0}{\sqrt{2}}(\hat{i}+\hat{j})$ is held fixed at the origin $O$ in the presence of a uniform electric field $\vec{E} = E_0 \hat{i}$. If the potential is constant on a circle of radius $R$ centered at the origin as shown in the figure,then the correct statement$(s)$ is/are:
($\varepsilon_0$ is the permittivity of free space,$R \gg$ dipole size)
$(1)$ $R = \left(\frac{p_0}{4 \pi \varepsilon_0 E_0}\right)^{1/3}$
$(2)$ The magnitude of the total electric field on any two points of the circle will be the same.
$(3)$ The total electric field at point $A$ is $\vec{E}_A = \sqrt{2} E_0(\hat{i}+\hat{j})$
$(4)$ The total electric field at point $B$ is $\vec{E}_B = 0$

An electric dipole consists of two opposite charges each of magnitude $1 \,\mu C$ separated by a distance of $2 \,cm$. The dipole is placed in an external field of $10^5 \,N/C$. The maximum torque on the dipole is ......... $Nm$.

An electric dipole of moment $p$ is placed in an electric field of intensity $E$. The dipole acquires a position such that the axis of the dipole makes an angle $\theta$ with the direction of the field. Assuming that the potential energy of the dipole is zero when $\theta = 90^o$,the torque and the potential energy of the dipole will respectively be

An electron and a proton are at a distance of $1\,\mathring{A}$. The dipole moment of this system will be in $(C \cdot m)$: