Equipotential surfaces

Two charges $Q_1=q$ and $Q_2=mq$ are placed at the points $P_1(a,b)$ and $P_2(ma,mb)$, respectively, in the $XY$ plane, where $a,b\ne0$ and $m\ne0,1$. If $V_1$ is the potential at a point in the $XY$ plane due to charge $Q_1$ and $V_2$ is the potential at that point due to charge $Q_2$. Correct statement(s) for the points at which $|V_1|=|V_2|$ is/are:

The value of $R$ is ____ meter.

The value of $b$ is ____ meter.

An electric dipole with dipole moment $\dfrac{p_0}{\sqrt2}(\hat i + \hat j)$ is held fixed at the origin O in the presence of an uniform electric field of magnitude $E_0$. If the potential is constant on a circle of radius $R$ centered at the origin as shown in figure, then the correct statement(s) is/are:

($\epsilon_0$ is permittivity of free space. $R \gg$ dipole size)

There is a uniform electrostatic field in a region. The potential at various points on a small sphere centred at P, in the region, is found to vary between the limits 589.0 V to 589.8 V. What is the potential at a point on the sphere whose radius vector makes an angle of 60° with the direction of the field ?

Within a spherical charge distribution of charge density ρ(r), N equipotential surfaces of potential $V_0$, $V_0+\Delta V$, $V_0+2\Delta V$, .......... $V_0+N\Delta V$ (ΔV > 0), are drawn and have increasing radii $r_0$, $r_1$, $r_2$, .......... $r_N$, respectively. If the difference in the radii of the surfaces is constant for all values of $V_0$ and ΔV then :

A uniformly charged solid sphere of radius R has potential $V_0$ (measured with respect to ∞) on its surface. For this sphere the equipotential surfaces with potentials $\dfrac{3V_0}2$, $\dfrac{5V_0}4$, $\dfrac{3V_0}4$ and $\dfrac{V_0}4$ have radius $R_1$, $R_2$, $R_3$ and $R_4$ respectively. Then