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 $\mu C$)?

$A$ disc of radius $R$ is charged on its surface with surface charge density $\sigma = \sigma_0 r^3$. Here $\sigma_0$ is a constant and $r$ is the distance from its centre. The total charge on the disc is:

Obtain the expression for the electric field at any point due to a continuous distribution of charge on a $(i)$ line,$(ii)$ surface,and $(iii)$ volume.

If on two concentric hollow spheres of radii $r$ and $R$ $(R > r)$,the total charge $Q$ is distributed such that their surface charge densities are equal,then the potential at their common centre 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.

$A$ circle of radius $a$ has a linear charge density given by $\lambda = \lambda_0 \cos^2 \theta$ on its circumference. What will be the total charge on the circle?