$A$ neutral ammonia $(NH_3)$ molecule in its vapour state has an electric dipole moment of magnitude $5 \times 10^{-30} \ C \cdot m$. How far apart are the molecule's centres of positive and negative charge?

When a test charge is brought in from infinity along the perpendicular bisector of an electric dipole,the work done is ..........

An electric dipole having each charge of magnitude $2 \mu C$ is placed in an electric field of intensity $8 \times 10^{4} \ N/C$. If the maximum torque acting on the dipole is $4 \times 10^{-3} \ N \cdot m$,the length of the dipole is: (in $mm$)

Two charges $+q$ and $-q$ are placed at a distance $b$ apart as shown in the figure. The electric field at a point $P$ on the perpendicular bisector as shown is

An electric dipole has a fixed dipole moment $\vec{P}$ which makes an angle $\theta$ with respect to the $x$-axis. When subjected to an electric field $\vec{E_1} = E\hat{i}$,it experiences a torque $\vec{T_1} = \tau\hat{k}$. When subjected to another electric field $\vec{E_2} = \sqrt{3}E\hat{j}$,it experiences a torque $\vec{T_2} = -\vec{T_1}$. The angle $\theta$ is .......$^o$.

The potential at a point due to an electric dipole will be maximum and minimum when the angles between the axis of the dipole and the line joining the point to the dipole are respectively: