The ratio of electric fields on the axis and at the equator of an electric dipole is

Write the formulas for the electric field due to an electric dipole and the magnetic field due to a current-carrying loop at a point on their respective equatorial (bisector) lines at a distance $x$.

Two small spherical balls of mass $10 \ g$ each with charges $-2 \ \mu C$ and $2 \ \mu C$,are attached to two ends of a very light rigid rod of length $20 \ cm$. The arrangement is now placed near an infinite nonconducting charge sheet with a uniform charge density of $100 \ \mu C / m^2$ such that the length of the rod makes an angle of $30^{\circ}$ with the electric field generated by the charge sheet. The net torque acting on the rod is (Take $\varepsilon_0 = 8.85 \times 10^{-12} \ C^2 / Nm^2$) (in $Nm$)

Charges $-q$ and $+q$ located at $A$ and $B$,respectively,constitute an electric dipole. Distance $AB = 2a$,$O$ is the midpoint of the dipole and $OP$ is perpendicular to $AB$. $A$ charge $Q$ is placed at $P$ where $OP = y$ and $y >> 2a$. The charge $Q$ experiences an electrostatic force $F$. If $Q$ is now moved along the equatorial line to $P'$ such that $OP' = \frac{y}{3}$,the force on $Q$ will be close to: $\left( \frac{y}{3} >> 2a \right)$

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 $\vec{E}_B = 0$

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: