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 $\mu C$)?

Each of two large conducting parallel plates has one-sided surface area $A$. If one of the plates is given a charge $Q$ whereas the other is neutral,then the electric field at a point in between the plates is given by

$A$ thin square plate is placed in the $x-y$ plane as shown in the figure,such that its center coincides with the origin. Its charge density at point $(x, y)$ is $\sigma = \sigma_0 xy$ (where $\sigma_0$ is a constant). Find the total charge on the plate.

The radius of a charged metal sphere $(R)$ is $10 \, cm$ and its potential is $300 \, V$. Find the charge density on the surface of the sphere.

Write an equation for the electric potential due to a linear charge distribution.

The surface charge density $\sigma$ on a charged conducting sphere of radius $R$ in terms of the electric field intensity $E$ at a distance $r$ $(r > R)$ in free space is (where $\varepsilon_{0}$ is the permittivity of free space):