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 $\mu C$)?

$A$ charge is spread non-uniformly on the surface of a hollow sphere of radius $R$,such that the charge density is given by $\sigma = \sigma_0(1 - \sin \theta)$,where $\theta$ is the usual polar angle. The potential at the centre of the sphere is

Explain linear charge density,surface charge density,and volume charge density for uniform charge distribution.

In the absence of other conductors,the surface charge density is:

$A$ point charge $q = 1 \mu C$ is located at a distance $2 \text{ cm}$ from one end of a thin insulating wire of length $L = 10 \text{ cm}$ having a charge $Q = 24 \mu C$,distributed uniformly along its length,as shown in the figure. The force between $q$ and the wire is . . . . . . $N$. (Use $\frac{1}{4 \pi \epsilon_0} = 9 \times 10^9 \text{ N} \cdot \text{m}^2 / \text{C}^2$)

Three concentric metallic spherical shells of radii $R, 2R, 3R$ are given charges $Q_1, Q_2, Q_3$ respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then,the ratio of the charges given to the shells,$Q_1 : Q_2 : Q_3$,is