Use Gauss’s law to find the magnitude of the electric field at a radius s away from the axis inside an infinite cylinder with uniform volume charge density ρ.

A long straight wire has fixed negative charge with a linear charge density of magnitude 4.8 nC/m. The wire is to be enclosed by a coaxial, thin-walled, nonconducting cylindrical shell of radius 1.2 cm. The shell is to have positive charge on its outside surface with a surface charge densitys that makes the net external electric field is zero. Calculate s.

A conducting hollow sphere of internal radius a and external b has a total charge + 11q, determine the electric field between radius a and b in terms of ɛ0, q and the radius of the Gaussian r.

A sphere shell of radius R, centered on the origin, has a uniform surface charge density /sigma and no charge in its interior. What is the magnitude of the electric field outside the sphere, at the distance r from the center, where r > R?