In the following diagram,the work done in moving a point charge from point $P$ to points $A$,$B$,and $C$ is $W_A$,$W_B$,and $W_C$ respectively. Then:

$A$ regular hexagon of side $9 \ cm$ has a charge $5 \mu C$ at each of its vertices. The electric potential at its centre is $..........V$. $(k = 9 \times 10^9 \ Nm^2 C^{-2})$

$A$ thin conducting spherical shell (center at $O$) having charge $Q_0$,radius $R$ and three point charges $Q_0$,$-2Q_0$,$3Q_0$ are kept at points $A$,$B$,and $C$ respectively as shown in the figure. Find the potential at any point on the conducting shell. (Potential at infinity is assumed to be zero)

The mass of a particle is $400$ times that of an electron and its charge is double that of an electron. The particle is accelerated by a potential difference of $5 \; V$. If the particle was initially at rest,what will be its final kinetic energy in $eV$?

An arc of radius $r$ carries a charge. The linear charge density is $\lambda$ and the arc subtends an angle of $\frac{\pi}{3}$ at the centre. What is the electric potential at the centre?

Three concentric spherical metallic shells $X$,$Y$,and $Z$ of radii $a$,$b$,and $c$ respectively $[a < b < c]$ have surface charge densities $\sigma$,$-\sigma$,and $\sigma$,respectively. The shells $X$ and $Z$ are at the same potential. If the radii of $X$ and $Y$ are $2\,cm$ and $3\,cm$,respectively,then the radius of shell $Z$ is $......\,cm$.