In the following diagram,the work done in moving a point charge from point $P$ to points $A, B$ and $C$ are $W_A, W_B$ and $W_C$ respectively. Then ($A, B, C$ are points on a semicircle and point charge $q$ is at the centre of the semicircle):

Charges of $2 \mu C$ and $-3 \mu C$ are placed at two points $A$ and $B$ separated by a distance of $1 \ m$. The distance of the point from $A$ where the net potential is zero is: (in $m$)

The potential at a point,due to a positive charge of $100\,\mu C$ at a distance of $9\,m$,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 $A$?

Two small equal point charges of magnitude $q$ are suspended from a common point on the ceiling by insulating massless strings of equal lengths. They come to equilibrium with each string making an angle $\theta$ from the vertical. If the mass of each charge is $m$,then the electrostatic potential at the centre of the line joining them will be $\left( \frac{1}{4\pi \epsilon_0} = k \right).$

If the potential of the inner shell of radius $r$ is $10\,V$ and that of the outer shell of radius $2r$ is $5\,V$, then the potential at the centre will be....$V$