An electric charge $10^{-6} \mu \mathrm{C}$ is placed at origin $(0,0)$ $\mathrm{m}$ of $\mathrm{X}-\mathrm{Y}$ co-ordinate system. Two points $\mathrm{P}$ and $\mathrm{Q}$ are situated at $(\sqrt{3}, \sqrt{3}) \mathrm{m}$ and $(\sqrt{6}, 0) \mathrm{m}$ respectively. The potential difference between the points $P$ and $Q$ will be :

Electric charges of $ + 10\,\mu C,\; + 5\,\mu C,\; - 3\,\mu C$ and $ + 8\,\mu C$ are placed at the corners of a square of side $\sqrt 2 \,m$. the potential at the centre of the square is

A neutral spherical copper particle has a radius of $10 \,nm \left(1 \,nm =10^{-9} \,m \right)$. It gets charged by applying the voltage slowly adding one electron at a time. Then, the graph of the total charge on the particle versus the applied voltage would look like

In a hollow spherical shell potential $(V)$ changes with respect to distance $(r)$ from centre

Two charges $3 \times 10^{-8}\; C$ and $-2 \times 10^{-8}\; C$ are located $15 \;cm$ apart. At what point on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.

The radius of a soap bubble whose potential is $16\,V$ is doubled. The new potential of the bubble will be.....$V$