A long, straight wire is surrounded by a hollow metal cylinder whose axis coincides with that of the wire. The wire has a charge per unit length of à, and the cylinder has a net charge per unit length of 21. From this information, use Gauss's law to find the following. (Assume the charge per unit length, à, is positive. Use any variable or symbol stated above along with the following as necessary: ɛo and r.) (a) the charge per unit length on the inner surface of the cylinder Ainner = (b) the charge per unit length on the outer surface of the cylinder Aouter= (c) the electric field outside the cylinder a distance r from the axis magnitude E = direction ---Select---

Below is a solid sphere of insulating materials (meaning that once placed, charge will not move around even when it feels a force).  This sphere has a changing charge density given by the equation below.  This tells you that there is more charge near the outer edges (when r is larger) then near the center (when r is small) since the charge density is proportional to r^2. In the image R is the total radius of the sphere and r is the distance from the center you will be asked about.  There values are below.  You have to calculate the amount of charge enclosed with the radius of r to find the electric field.  You'll need to integrate to do this - that's where the charge density equation below will be used. Use Gauss's Law to find the Electric Field magnitude at a distance r from the center of the sphere.  Make sure to think about charge enclosed and how to find it.  It is a little more complicated in this problem.  Be careful with your 2 radial values (R and r).

Please write all details and properties. I would much appreciate it a lot. Any property or remark, regardless of how insignificant, please include in the answer. Thank you very much.

Please don't provide handwritten solution.