For a point charge,the electric potential and electric field at a given point are $600 \, V$ and $200 \, N/C$ respectively. The magnitude of the point charge is ......... $\mu C$.

$(a)$ Calculate the potential at a point $P$ due to a charge of $4 \times 10^{-7} \; C$ located $9 \; cm$ away.
$(b)$ Hence,obtain the work done in bringing a charge of $2 \times 10^{-9} \; C$ from infinity to the point $P$. Does the answer depend on the path along which the charge is brought?

$A$ charge $+q$ is distributed over a thin ring of radius $r$ with line charge density $\lambda = q \sin^2 \theta / (\pi r)$. Note that the ring is in the $XY$-plane and $\theta$ is the angle made by the position vector with the $X$-axis. The work done by the electric force in displacing a point charge $+Q$ from the centre of the ring to infinity is

Eight equal charges $q$ are placed at each corner of a cube of side $a$. The work done in carrying a charge $-q$ from its centre to infinity is:

An electrostatic paint sprayer has a metal sphere of diameter $18 \, cm$ and at a potential of $25 \, kV$. The charge on the metal sphere is: (in $ \, \mu C$)

$A$ 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: