Three identical charges of $10 \ \mu C$ are placed at the vertices of an equilateral triangle of side $10 \ cm$. The electrostatic potential energy of the system is ....... $J$.

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

$A, B$ and $C$ are three points in a uniform electric field as shown in the figure. The electric potential is

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 $A$?

Three concentric charged metallic spherical shells $A$,$B$,and $C$ have radii $a$,$b$,and $c$ (where $a < b < c$) and surface charge densities $+\sigma$,$-\sigma$,and $+\sigma$ respectively. The potential $V_A$ at the surface of shell $A$ is ($\epsilon_0$ = permittivity of free space).

The figure shows a solid hemisphere with a charge of $5 \ nC$ distributed uniformly throughout its volume. The hemisphere lies on a plane and point $P$ is located on this plane,along a radial line from the center of curvature at a distance of $15 \ cm$. The electric potential at point $P$ due to the hemisphere is ..... $V$.