There is a uniform electrostatic field in a region. The potential at various points on a small sphere centered 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 $60^o$ with the direction of the field (in $,V$)?

Eight charges,each of magnitude $q$,are placed at the vertices of a cube placed in a vacuum. The electric potential at the centre of the cube due to this system of charges is . . . . . . . ($\varepsilon_0 = $ permittivity of vacuum,$a = $ length of each side of the cube.)

If four charges $q_1 = +1 \times 10^{-8} \text{ C}$, $q_2 = -2 \times 10^{-8} \text{ C}$, $q_3 = +3 \times 10^{-8} \text{ C}$, and $q_4 = +2 \times 10^{-8} \text{ C}$ are kept at the four corners of a square of side $1 \text{ m}$, then the electric potential at the centre of the square is: (in $\text{ V}$)

Figures $(a)$ and $(b)$ show the field lines of a positive and negative point charge respectively.
$(a)$ Give the signs of the potential difference $V_{P}-V_{Q}$ and $V_{B}-V_{A}$.
$(b)$ Give the sign of the potential energy difference of a small negative charge between the points $Q$ and $P$,and $A$ and $B$.
$(c)$ Give the sign of the work done by the field in moving a small positive charge from $Q$ to $P$.
$(d)$ Give the sign of the work done by the external agency in moving a small negative charge from $B$ to $A$.
$(e)$ Does the kinetic energy of a small negative charge increase or decrease in going from $B$ to $A$?

$A$ charge of $10^{-3} \ \mu C$ is placed at the origin $(0, 0)$ of an $X-Y$ coordinate system. Two points $A$ and $B$ are located at $(\sqrt{2}, \sqrt{2})$ and $(2, 0)$ respectively. The potential difference between points $A$ and $B$ is ....... $V$.

The variation of electrostatic potential $V$ with radial distance $r$ from the centre of a positively charged metallic thin shell of radius $R$ is given by the graph: