A Positively Charged Cylinder with Nonuniform Volume Charge Density

Overview of a Positively Charged Cylinder

A very long, solid, positively charged cylinder has a radius RR and is made of a nonconducting material. The nonuniform volume charge density is given by rho=+ar, where r is the radial distance away from the long central axis of the cylinder.

Final Answer

A positively charged cylinder with a nonuniform volume charge density has a varying charge density as a function of the radial distance from the central axis of the cylinder. The charge density increases or decreases depending on the value of the constant a in the expression rho=+ar. The cylinder is made of a nonconducting material, which means that the charge distribution remains fixed and does not redistribute itself.

Explanation

A positively charged cylinder is a cylindrical object that carries a positive charge. The radius of the cylinder is denoted by R. The volume charge density, denoted by rho, represents the amount of charge per unit volume. In this case, the volume charge density is nonuniform and given by rho=+ar, where r is the radial distance away from the long central axis of the cylinder.

The nonuniform volume charge density indicates that the charge density varies as a function of the radial distance from the axis of the cylinder. As the radial distance increases, the charge density increases or decreases depending on the value of the constant a. The positive sign in the expression rho=+ar indicates that the charge is positive throughout the cylinder.

It is important to note that the cylinder is made of a nonconducting material, which means that the charge is not able to move freely within the cylinder. This implies that the charge distribution remains fixed and does not redistribute itself.