$A$ uniformly charged conducting sphere of $2.4 \, m$ diameter has a surface charge density of $80.0 \, \mu C m^{-2}$. The charge on the sphere is nearly

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.

$A$ particle of mass $2 \times 10^{-6} \ kg$ with a charge $5 \times 10^{-6} \ C$ is hanging in air above a similarly charged conducting surface. The charge density of the surface is (Assume $\epsilon_0 = 8.85 \times 10^{-12} \ C^2 N^{-1} m^{-2}$ and $g = 10 \ m \ s^{-2}$)

Find the surface charge density at the intersection of the plane $x = 3 \, m$ and the $x$-axis,given a uniform line charge of $8 \, nC/m$ lying along the $z$-axis in free space.

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

$A$ 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.