A charge $+q$ is distributed over a thin ring of radius $r$ with line charge density $\lambda =q{\sin }^2\theta /\left(\pi r\right)$. Note that the ring is in the $x-y$ plane and $\theta$ is the angle made by $r$ with the $x$-axis. The work done by the electric force in displacing a point charge $+Q$ from the center of the ring to infinity is
4. .

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