A thin ring made of insulating material has radius $R$. Total charge on the ring is $6\mu \mathrm{C}$. The ring is now placed horizontally above a grounded solid metal sphere of radius $r$, so that the centre of the ring and the top of the sphere coincide. The total charge induced on the sphere (in $\mu \mathrm{C}$) is ? Consider $R=2\sqrt{2}r$

A charge Q is distributed over two concentric conducting thin spherical shells radii $\mathrm{r}$ and $\mathrm{R} \left(\mathrm{R}>\mathrm{r}\right)$. If the surface charge densities on the two shells are equal, the electric potential at the common centre is : 

Four point charge (with equal magnitude of charge of $5 C;$ but with different signs) are placed at four corners of a square of side $10 \mathrm{m}.$ Assuming that the square is centered at the origin and the configuration of the charges are as given in the figure, the potential and the magnitude of electric field at the origin, respectively are

[Note $\left.k=\frac{1}{4\pi {\epsilon }_0}\right]$