An electric charge $10^{-8} \ C$ is placed at the point $(4 \ m, 7 \ m, 2 \ m)$. At the point $(1 \ m, 3 \ m, 2 \ m)$,the electric

$A$ charge $Q$ is uniformly distributed over a rod $AB$ of length $L$ as shown in the figure. The electric potential at point $O$,which is at a distance $L$ from end $A$,is:

$A$ solid sphere of radius $R$ is charged uniformly. At what distance from its surface is the electrostatic potential half of the potential at the centre?

Along the $x$-axis,three charges $\frac{q}{2}, -q$ and $\frac{q}{2}$ are placed at $x=0, x=a$ and $x=2a$ respectively. The resultant electric potential at a point $P$ located at a distance $r$ from the charge $-q$ $(r > a)$ is ($\varepsilon_0$ is the permittivity of free space):

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):

Four identical charges $+50\,\mu C$ each are placed,one at each corner of a square of side $2\,m$. How much external energy is required to bring another charge of $+50\,\mu C$ from infinity to the centre of the square? (Given $\frac{1}{4\pi\varepsilon_0} = 9 \times 10^9\,\frac{N\cdot m^2}{C^2}$)