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:

Two short dipoles $A$ and $B$, $A$ having charges $\pm 2 \mu C$ and length $1 \text{ cm}$, and $B$ having charges $\pm 4 \mu C$ and length $1 \text{ cm}$, are placed with their centres $80 \text{ cm}$ apart as shown in the figure. The electric field at a point $P$, equidistant from the centres of both dipoles, is . . . . . . $\text{N/C}$.

Write the equation for the electric field produced by an electric dipole at a point on its equatorial line,given the condition $r >> a$ (where $r$ is the distance from the center and $2a$ is the dipole length).

An electric dipole is placed at an angle of $30^{\circ}$ with an electric field of intensity $2 \times 10^5\,N C^{-1}$. It experiences a torque equal to $4\,N m$. Calculate the magnitude of charge on the dipole,if the dipole length is $2\,cm$. (in $,mC$)

Six charges are placed at the vertices of a regular hexagon as shown in the figure. The electric field on the line passing through point $O$ and perpendicular to the plane of the figure at a distance of $x (>> a)$ from $O$ is

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 $\vec{E}_B = 0$