The electric flux is $\phi = \alpha \sigma + \beta \lambda$,where $\lambda$ and $\sigma$ are linear and surface charge density,respectively. The ratio $\left(\frac{\alpha}{\beta}\right)$ represents:

$A$ point charge $q$ is situated at a distance $r$ on the axis from one end of a thin conducting rod of length $L$ having a charge $Q$ (uniformly distributed along its length). The magnitude of the electric force between the two is . . . . . . .

Obtain the formula for the electric field due to a long thin wire of uniform linear charge density $\lambda$ without using Gauss's law.

How much charge should be placed on a spherical shell of radius $25 \ cm$ to have a surface charge density of $\frac{3}{\pi} \mu C/m^2$ (in $\mu C$)?

$A$ non-uniformly shaped conductor is charged. Then,at its sharpest point:

$A$ spherical conducting shell of inner radius $r_1$ and outer radius $r_2$ has a net charge $Q$. $A$ point charge $-q$ is placed at the center of the shell. Determine the surface charge density on the inner and outer surfaces of the shell.