Two points $P$ and $Q$ are maintained at the potentials of $10\  V$ and $- 4\ V$, respectively. The work done in moving $100$ electrons from $P$ to $Q$ is

$(a)$ 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?

If identical charges $( - q)$ are placed at each corner of a cube of side $b$, then electric potential energy of charge $( + q)$ which is placed at centre of the cube will be

A particle of mass $‘m’$ and charge $‘q’$ is accelerated through a potential difference of $V$ volt, its energy will be

In the figure, the inner (shaded) region $A$ represents a sphere of radius $r_A=1$, within which the electrostatic charge density varies with the radial distance $r$ from the center as $\rho_A=k r$, where $k$ is positive. In the spherical shell $B$ of outer radius $r_B$, the electrostatic charge density varies as $\rho_{\bar{B}}=\frac{2 k}{r}$. Assume that dimensions are taken care of. All physical quantities are in their $SI$ units.

Which of the following statement($s$) is(are) correct?

On moving a charge of $20$ coulombs by $2 \;cm , 2 \;J$ of work is done, then the potential difference between the points is (in $volt$)