Figure, shown above, shows three situations involving a charged particle and a uniformly charged spherical shell. The charges and radii of the shells are indicated in the figure. If $F_1,F_2$ and $F_3$ are the magnitudes of the forces on the particle due to the presence of the shell in situations $\left(\mathrm{I}\right),\left(\mathrm{II}\right)$ and $\left(\mathrm{III}\right)$ respectively then

Two semicircular rings lying in same plane, of uniform linear charge density $\lambda$ have radius $r$ and $2r$. They are joined using two straight uniformly charged wires of linear charge density $\lambda$ and length $r$ as shown in figure. The magnitude of electric field at common centre of semi circular rings is

Figure above shows a closed Gaussian surface in the shape of a cube of edge length $3.0 \mathrm{m}$. There exists an electric field given by $\overrightarrow{E}=[\left(2.0x+4.0\right)\hat{\mathrm{i}}+8.0\hat{\mathrm{j}}+3.0\hat{\mathrm{k}}] \mathrm{N} {\mathrm{C}}^{-1}$, where $x$ is in metres, in the region in which it lies. The net charge in coulombs enclosed by the cube is equal to