A thin, metallic spherical shell contains a charge Q on it. A point charge q is placed at the centre of the shell and another charge $q_1$ is placed outside it as shown in figure. All the three charges are positive. The force on the charge at the centre is

Linear charge density of a half ring varies with $\text{θ}$ as $\lambda ={\lambda }_0\cos \text{θ}.$ Then find the total charge on the ring.

If linear charge density of a wire of length $L$ depends on distance $x$ from one end as $\text{λ}=\frac{{\text{λ}}_{0}x}{L},$ then find the total charge on the wire.

The Gaussian surface used for calculating the electric field due to a charge distribution is

A linear charge rod having linear charge density $\lambda$ penetrates a cube diagonally and then, it penetrates a sphere diametrically as shown. What will be the ratio of flux coming out of cube and sphere?