$A$ 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?

Three identical metal plates with large surface areas are kept parallel to each other as shown in the figure. The leftmost plate $A$ is given a charge $Q$ and the rightmost plate $C$ is given a charge $-2Q$. The middle plate $B$ is neutral. Then the charge appearing on the outer surface $S$ of the plate $C$ is:

Give definitions of linear,surface,and volume charge densities and write their $SI$ units.

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.

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):

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